Center for Material Science
The Center for Materials Science is devoted to the chemical materials analysis and to mathematical modelling in the context materials science.
Thematic Fields
Material Analysis
The team of the thematic field of materials analysis focuses on carrying out chemical material analysis using chemical spectroscopic methods available in-house. In addition to chemical characterization of oxidation processes and other material changes, we can determine very precise flow properties of liquids and pasty substances, also in combination with detection of molecular material changes in the course of shearing processes. We also offer advice and contac persons on suitable analysis methods.
Methodes
Spectroscopic characterization of the chemical bonds of oils, fats and polymer materials using vibrational spectroscopy methods
- Infrared (IR) spectroscopy
- Raman spectroscopy
Both methods supplement each other in terms of information content.
Spectroscopic determination of metallic atoms (all metals heavier than sodium) in liquid and solid samples using X-ray fluorescence analysis (XRF).
Rheological-spectroscopic determination of the pot life of resins and paints. The parallel detection of the Raman vibration spectra and the change in viscosity of the mixed substances allows a very precise determination of the polymerization time under constant temperature conditions.
Rheological determination of oil and fat viscosities.
Determination of friction values for material pairings.
Computed tomographic (CT) determination of material inhomogeneity (foreign bodies / air pockets).
Projects
Vib-HVDC: Vibration spectroscopic analysis of E-field induced transformer oil movement
Using Raman spectroscopy, non-polar mode oscillations can be detected without contact. Transformer oil molecules that are exposed to an external electric field align themselves in the field. This dipole-induced alignment of the hydrocarbon molecules is expressed in changes in the intensity of certain Raman vibration bands.
The research project aims to investigate the alignment behavior of transformer oils depending on the water content and oil composition. Furthermore, it contributes to clarifying the influence of paper as an electrode cover on oil molecule mobility. Results of this study are complementary to optical Kerr measurements and contribute to the interpretation of oil conductivity behavior.


Relaxed: Raman-based detection of the relaxation time of shear-induced material stresses
Mechanical shearing or high-frequency E-fields induce molecular movements in the material, which lead to an increase in the Raman background signal. Through time-resolved detection of the Raman signal intensity, we can determine the relaxation time due to shear without contact. The aim of the research project is to explain the currently unknown phenomenon of the shear-induced Raman signal increase.


Contact:
Prof. Dr. Kai Diethelm
97421 Schweinfurt
* during the lecture period: Monday, 11:45-12:45, in room 1.E.41.3
* during the lecture-free period: by appointment
Supervision Informatics
Head of Scientific Computing Lab
Head, Laboratory for Scientific Computing
Ombudsperson for Good Scientific Practice

Teaching Areas
Lehrgebiete
Mathematik
Angewandte Informatik
Publications
ORCID
My ORCID-ID: 0000-0002-7276-454X
Peer-Reviewed Publications in Scientific Journals and Collections
1994-2017
For a list of my works published before my move to THWS, see here.
2018
- (with N. J. Ford)
A Note on the Well-posedness of Terminal Value Problems for Fractional Differential Equations.
J. Integral Equations Appl. 30 (2018), 371-376.
Abstract and link to full text - Numerical Methods for the Fractional Differential Equations of Viscoelasticity.
In H. Altenbach, A. Öchsner (Eds.): Encyclopedia of Continuum Mechanics. Springer, Berlin, 2018.
Abstract and link to full text
2019
- General Theory of Caputo-Type Fractional Differential Equations.
In A. Kochubei, Y. Luchko (Eds.): Handbook of Fractional Calculus with Applications, Vol. 2: Fractional Differential Equations.
De Gruyter, Berlin, 2019, pp. 1-20.
Abstract and link to full text - Fundamental Approaches for the Numerical Handling of Fractional Operators and Time-Fractional Differential Equations.
In G. E. Karniadakis (Ed.): Handbook of Fractional Calculus with Applications, Vol. 3: Numerical Methods.
De Gruyter, Berlin, 2019, pp. 1-22.
Abstract and link to full text
2020
- (with P. G. Kjeldsberg, R. Schöne, M. Gerndt, L. Riha, V. Kannan, M.-C. Sawley, J. Zapletal, A. Gocht, N. Reissmann, O. Vysocki, M. Kumaraswamy & W. E. Nagel)
Run-time Exploitation of Application Dynamism for Energy-efficient Exascale Computing.
In F. Catthoor, T. Basten, N. Zompakis, M. Geilen & P. G. Kjeldsberg (Eds.): System-Scenario-based Design Principles and Applications.
Springer International, Cham (2020), 113-126.
Abstract and link to full text - (mit R. Garrappa & M. Stynes)
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus.
Mathematics 8 (2020), Article No. 324.
Abstract
Full text (PDF) - (with R. Garrappa, A. Giusti & M. Stynes)
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used.
Fract. Calc. Appl. Anal. 23 (2020), 610-634.
Abstract and link to full text
Full text at arXiv.org
2021
- Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
In Proc. 9th International Conference on Systems and Control (ICSC 2021).
IEEE, Piscataway, 2021, pp. 455-460.
Full text - (with M. Kumaraswamy, A. Chowdhury, A. Gocht, J. Zapletal, L. Riha, M.-C. Sawley, M. Gerndt, N. Reissmann, O. Vysocky, O. Bouizi, P. G. Kjeldsberg, R. Carreras, R. Schöne, U. S. Mian, V. Kannan & W. E. Nagel)
Saving Energy Using the READEX Methodology.
In H. Mix, C. Niethammer, H. Zhou, W. E. Nagel & M. M. Resch (Eds.): Tools for High Performance Computing 2018/2019.
Springer, Cham (2021), 27-53.
Full text
2022
- (with K. Kitzing, R. Picard, S. Siegmund, S. Trostorff & M. Waurick)
A Hilbert Space Approach to Fractional Differential Equations.
J. Dyn. Differ. Equations 34 (2022), 481-504.
Full text - (with V. Kiryakova, Y. Luchko, J. A. T. Machado & V. E. Tarasov)
Trends, directions for further research, and some open problems of fractional calculus.
Nonlinear Dynam. 107 (2022), 3245-3270.
Full text - (with H. T. Tuan)
Upper and lower estimates for the separation of solutions to fractional differential equations.
Fract. Calc. Appl. Anal., 25 (2022), 166-180
Full text - A new diffusive representation for fractional derivatives, Part II: Convergence analysis of the numerical scheme.
Mathematics 10 (2022), Article No. 1245.
Full text - (with H. D. Thai & H. T. Tuan)
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems.
Fract. Calc. Appl. Anal. 25 (2022), 1324-1360.
Full text - (with S. B. Damelin)
An analytic and numerical analysis of weighted singular Cauchy integrals with exponential weights on R.
Numer. Funct. Anal. Optim. 43 (2022), 1538-1577.
Full text
2023
- A new diffusive representation for fractional derivatives, Part I: Construction, implementation and numerical examples.
In A. Cardone, M. Donatelli, F. Durastante, R. Garrappa, M. Mazza & M. Popolizio (Eds.): Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers.
Springer Nature, Singapore, 2023, pp. 1-15.
Full text - Diffusive representations for the numerical evaluation of fractional integrals.
To appear in Proc. 2023 International Conference on Fractional Differentiation and its Applications.
IEEE, Piscataway, 2023.
Full text - (with F. Uhlig)
A new approach to shooting methods for terminal value problems of fractional differential equations.
J. Sci. Comput. 97 (2023), Article No. 38.
Full text
MATLAB source code of associated software
2024
- (with R. Chaudhary & S. Hashemishahraki)
On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$.
Appl. Numer. Math. 203 (2024), 84-96.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
A constructive approach for investigating the stability of incommensurate fractional differential systems.
J. Math. Anal. Appl. 540 (2024), Article No. 128642.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
Stability properties of multi-order fractional differential systems in 3D.
IFAC PapersOnLine 58-12 (2024), 231–236.
Corrigendum: arXiv:2312.10653.
Volltext - (with R. Chaudhary)
Novel variants of diffusive representation of fractional integrals: Construction and numerical computation.
IFAC PapersOnLine 58-12 (2024), 412-417.
Volltext - (with R. Chaudhary)
Revisiting diffusive representations for enhanced numerical approximation of fractional integrals.
IFAC PapersOnLine 58-12 (2024), 418-423.
Volltext - Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives.
To appear in J. Ball, H.-O. Tylli & J. A. Virtanen (Eds.): Recent Developments in Operator
Theory, Mathematical Physics and Complex Analysis—IWOTA 2023, Helsinki. Birkhäuser, Cham.
Preprint: arXiv:2402.03487.
MATLAB source code of associated software
2025
Books
- The Analysis of Fractional Differential Equations — An application-oriented exposition using differential operators of Caputo type.
Springer, Berlin (2010), viii+247 pp., ISBN 978-3-642-14573-5. - (with D. Baleanu, E. Scalas and J. J. Trujillo)
Fractional Calculus — Models and numerical methods.
First edition, World Scientific Publ. Comp., Singapore (2012), xxiv+400 pp., ISBN 978-981-4355-20-9.
Second edition, World Scientific Publ. Comp., Singapore (2016), xxviii+448 pp., ISBN 978-981-3140-03-5. - Gemeinschaftliches Entscheiden — Untersuchung von Entscheidungsverfahren mit mathematischen Hilfsmitteln.
Springer, Berlin (2016), ix+138 pp., ISBN 978-3-662-48779-2.
(in German)
Conference Presentations
2018
- Fractional-Order Models for the Behaviour of Concrete Under Mechanical Load Over Very Long Time Intervals.
Workshop on Fractional Calculus and Applications, University of Potsdam, September 06-07, 2018 (invited plenary talk).
2019
- (a) Fractional Ordinary Differential Equations.
(b) Nonclassical Methods for the Numerical Solution of Fractional Differential Equations.
(c) Numerical Methods for Terminal Value Problems of Fractional Order.
COST Action 15225 Training School, Politecnico di Bari, Italy, July 22-26, 2019 (invited plenary talks).
2020
- Fast Computation of Fractional Integrals and its Application.
4th Conference on Numerical Methods for Fractional-Derivative Problems, Beijing Computational Science Research Center, Beijing, China, October 22-24, 2020 (invited talk; online).
2021
- Numerical Methods for Terminal Value Problems of Fractional Order.
Irish Numerical Analysis Forum, University of Limerick, Ireland, June 17, 2021 (invited talk; online). - Terminal Value Problems for Fractional Differential Equations and Their Numerical Solution.
ALOP Workshop on Nonlocal Models, University of Trier, July 12-14, 2021 (online). - Fast and Memory Efficient Solution Methods for Fractional Ordinary Differential Equations.
Joint Annual Meeting of the German Mathematicians' Union and the Austrian Mathematical Society, University of Passau, Germany, September 27 - October 01, 2021 (online). - Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
9th International Conference on Systems and Control (ICSC'2021), École Nationale Supérieure d'Ingénieurs de Caen, France, November 24-26, 2021 (online). - Stability Questions for Fractional Differential Equations.
Seminar on Dynamical Systems and Control theory, University of Würzburg, December 10, 2021 (invited talk).
2022
- Numerical Aspects of the Infinite State Representation of Fractional Differential Operators.
Computation, Analysis and Applications of PDEs with Nonlocal and Singular Operators, National University of Singapore, February 04 - March 04, 2022 (invited talk, online). - Diffusive Representations of Fractional Differential Operators and Their Use in Numerical Fractional Calculus.
Research Programme on Fractional Differential Equations, Isaac Newton Institute, University of Cambridge, UK, March 07, 2022 (invited talk, online).
2023
- Diffusive Representations for Fractional Integral Operators and Their Applications.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, February 10-11, 2023 (Poster; in German). - Diffusive Representations for the Numerical Evaluation of Fractional Integrals.
2023 International Conference on Fractional Differentiation and its Applications, Ajman University, United Arab Emirates, March 14-16, 2023 (online). - Terminal Value Problems for Fractional Ordinary Differential Equations: Analytical Properties of Their Solutions and an Efficient Numerical Algorithm.
International Workshop on Operator Theory and its Applications, Universität Helsinki, Finnland, July 31-August 04, 2023. - Efficient Handling of Fractional Order Material Laws in Finite Element Simulations.
Innovations in Fractional Calculus and Applications to Functional and Biological Materials, Centre Européen de Calcul Atomique et Moléculaire, EPF Lausanne, Switzerland, September 13-15, 2023 (invited talk). - Use of Novel Materials in the Production of Railway Sleepers.
Workshop on Sustainability, TH Würzburg-Schweinfurt and VDI, Schweinfurt, September 19,2023. - Stability Results for Multi-Order Fractional Differential Equation Systems.
International Workshop on Analysis and Numerical Approximation of Singular Problems, Peso da Régua, Portugal, 12.-14.10.2023 (invited plenary talk).
2024 - (α_1, α_2, . . . , α_n)-Eigenvalues of (n × n) Matrices: Applications, First Results, and Open Questions.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, 09.-10.02.2024 (Poster). - ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
Gauss Alliance HPC-Status Conference, TU Dresden, April 24-26, 2024. - (with S. A. Mohammadi, S. Burak, J. A. Reuter, L. Moj, K. Kassem-Manthey, B. Mohr, C. Terboven, F. Wolf & C. Woll) ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
ISC High Performance 2024, Hamburg, 12.-16.05.2024 (Poster). - Fast Numerical Algorithms for the Evaluation of Riemann-Liouville Integrals.
27th International Conference on Mathematical Modelling and Analysis, University of Tartu, Estonia, 28.-31.05.2024 (invited plenary talk). - The Approximation of Power Functions with Exponents in (-1, 0) by Sums of Exponentials and Its Applications.
Approximation Theory: Methods and Applications 2024, Università del Salento, Lecce, Italy, June 11-14, 2024 (invited plenary talk). - Efficient Algorithms for Computing Fractional Integrals.
Fractional Calculus Seminar, SISSA International School of Advanced Studies, Triest, Italy, June 28, 2024 (invited talk; online). - Diffusive Representations of Fractional Integral Operators and Their Applications.
12th International Conference on Fractional Differentiation and its Applications, Bordeaux, France, July 09-12, 2024 (plenary talk). - Integrals over R with Strongly Asymmetric Weights and Their Approximation in the Context of Numerical Solution Methods for Weakly Singular Volterra Equations.
6th Dolomites Workshop on Constructive Approximation and Applications, Alba di Canazei, Italien, 09.–13-09.2024 (invited keynote lecture). - AI-driven Design Parameter Optimization for Sheet Metal Forming Processes.
NAFEMS NORDIC Conference on AI and ML in Simulation Driven Design, Lund, Sweden, November 20–21, 2024.
Career
Biography
- 1992: Diploma in Mathematics, TU Braunschweig
- 1992-1998: Scientific Assistant, Institute of Mathematics, University of Hildesheim
(PhD in Computer Science 1994; Habilitation in Mathematics 1998) - 1998-2004: (Senior) Scientific Assistant, Department of Numerical Mathematics, TU Braunschweig
(Adjunct Professor since 2002) - 1999-2000: Temporary Professor for Numerical Mathematics, University of Gießen
- 2004-2018 Software developer and project coordinator, GNS Gesellschaft für numerische Simulation mbH, Braunschweig
- since 2018: Professor for Mathematics and Applied Computer Science, Technical University of Applied Sciences Würzburg-Schweinfurt
Additional Information
MINT-Tag Mainfranken 2021
Folien zum Vortrag "Die Mathematik der Demokratie"
Dokument(e)
MINT-Tag_Mainfranken.pdfMultiscale Modeling
Multiscale modeling aims for descriptions of materials properties across length scales, starting with chemical processes via molecular dynamics to macroscopic properties such as thermal conductivities. Our expertise: we can simulate chemical, micro- and macroscopic dynamic processes under the influence of external fields, e.g. electric fields, such as those occuring in battery cells, electrolysis / fuel cells and insulating materials. The insight from the modeling results lead to targeted materials optimisation. A powerful computing cluster is available for the numerical implementation.
Methods
The partial differential equations of elasticity theory or (electro)hydrodynamics lead to macroscopic descriptions of solids and fluids. The corresponding materials constants are typically spatial average values or correlation functions of microscopic quantities.
In the case of electrolyte solutions, e.g. contaminated insulator oils or battery fluids, the Poisson-Nernst-Planck theory provides a mesoscopic description of the dynamics. This provides access to quantities such as the DC-conductivity or the impedance so that macroscopic RC models are dispensable.
A microscopic description of the spatial structure of non-uniform liquids on the length scale of molecular diameters is possible using classical density functional theory (DFT), within which, in partiular, short-range intermolecular interactions can be taken into account. This description on molecular length scales requires technically complex nonlinear integral equations, the solution of methods for which we have many years of experience in.
Chemical reactions, such as redox reactions at metal-fluid interfaces or dissociation reactions, are modeled in the working group by using quantum mechanical density functional theory (DFT), which can resolve the molecular structure on atomic length scales. This allows for the calculation of reaction rates and reaction paths, even under the influence of external E-fields.
Projects
First global modeling of the conductivity behavior of transformer oils from the molecule to the current curve
The properties of application-relevant material systems are often characterized by an interaction of processes on different length scales. For example, if the Joule heat from high-voltage transformers (dimensions 0.1-10 m) is to be dissipated using insulating oil, the latter is usually separated from the metal of the transformer windings using insulating paper (thickness 10-100 µm). The electric field present in the pores of the insulating paper (diameter 10-100 nm) leads to various molecular processes (chemical bond length 100 pm) such as redox reactions, field-enhanced dissociation and electrical breakdown. The correct functioning of the transformer is determined, among other things, by the quality of the oil, whose insulating properties can decrease over time due to the molecular processes mentioned.
In order to technically control (if necessary avoid) such changes in properties, a comprehensive understanding of the interplay of the processes relevant to materials science on the individual length scales is of crucial importance.

The greater the spatial separation of the occupied and unoccupied molecular orbitals under consideration, the more strongly the molecule is polarized by the electric field, which in turn causes the tendency to split into ionic compounds. At 100 kV/mm the strongest polarization results when the field acts parallel to the terminal bond (c).
Structure of ionic fluids on inhomogeneously charged surfaces
With the help of electric fields that arise between charged surfaces, the structure of fluids, i.e. the distribution of molecules, can be easily influenced, which can be used, e.g., to modify the interfacial tension (electrowetting) or to control chemical reactions (electrolysis or batteries). Since the concentration of ionic components in fluids can be tiny but it does not vanish exactly, electrostatic fields in the absence of currents are shielded inside the fluid. For uniform surface charge distributions, the relevant decay length is given by the Debye length λ, which depends on the ion concentration and which can be, e.g., 1 µm in pure water, many 100 µm in purified organic solvents and less than 1 nm in concentrated electrolyte solutions. The fundamental question arises as to how far an arrangement of fluid molecules created by a uniform distribution of surface charges can extend into the interior. Information about this distribution of fluid molecules is crucial, e.g., for the design of supercapacitor, in which the capacitive properties of the arrangement of ions close to the surface are exploited.

Contact
Prof. Dr. Kai Diethelm
97421 Schweinfurt
* during the lecture period: Monday, 11:45-12:45, in room 1.E.41.3
* during the lecture-free period: by appointment
Supervision Informatics
Head of Scientific Computing Lab
Head, Laboratory for Scientific Computing
Ombudsperson for Good Scientific Practice

Teaching Areas
Lehrgebiete
Mathematik
Angewandte Informatik
Publications
ORCID
My ORCID-ID: 0000-0002-7276-454X
Peer-Reviewed Publications in Scientific Journals and Collections
1994-2017
For a list of my works published before my move to THWS, see here.
2018
- (with N. J. Ford)
A Note on the Well-posedness of Terminal Value Problems for Fractional Differential Equations.
J. Integral Equations Appl. 30 (2018), 371-376.
Abstract and link to full text - Numerical Methods for the Fractional Differential Equations of Viscoelasticity.
In H. Altenbach, A. Öchsner (Eds.): Encyclopedia of Continuum Mechanics. Springer, Berlin, 2018.
Abstract and link to full text
2019
- General Theory of Caputo-Type Fractional Differential Equations.
In A. Kochubei, Y. Luchko (Eds.): Handbook of Fractional Calculus with Applications, Vol. 2: Fractional Differential Equations.
De Gruyter, Berlin, 2019, pp. 1-20.
Abstract and link to full text - Fundamental Approaches for the Numerical Handling of Fractional Operators and Time-Fractional Differential Equations.
In G. E. Karniadakis (Ed.): Handbook of Fractional Calculus with Applications, Vol. 3: Numerical Methods.
De Gruyter, Berlin, 2019, pp. 1-22.
Abstract and link to full text
2020
- (with P. G. Kjeldsberg, R. Schöne, M. Gerndt, L. Riha, V. Kannan, M.-C. Sawley, J. Zapletal, A. Gocht, N. Reissmann, O. Vysocki, M. Kumaraswamy & W. E. Nagel)
Run-time Exploitation of Application Dynamism for Energy-efficient Exascale Computing.
In F. Catthoor, T. Basten, N. Zompakis, M. Geilen & P. G. Kjeldsberg (Eds.): System-Scenario-based Design Principles and Applications.
Springer International, Cham (2020), 113-126.
Abstract and link to full text - (mit R. Garrappa & M. Stynes)
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus.
Mathematics 8 (2020), Article No. 324.
Abstract
Full text (PDF) - (with R. Garrappa, A. Giusti & M. Stynes)
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used.
Fract. Calc. Appl. Anal. 23 (2020), 610-634.
Abstract and link to full text
Full text at arXiv.org
2021
- Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
In Proc. 9th International Conference on Systems and Control (ICSC 2021).
IEEE, Piscataway, 2021, pp. 455-460.
Full text - (with M. Kumaraswamy, A. Chowdhury, A. Gocht, J. Zapletal, L. Riha, M.-C. Sawley, M. Gerndt, N. Reissmann, O. Vysocky, O. Bouizi, P. G. Kjeldsberg, R. Carreras, R. Schöne, U. S. Mian, V. Kannan & W. E. Nagel)
Saving Energy Using the READEX Methodology.
In H. Mix, C. Niethammer, H. Zhou, W. E. Nagel & M. M. Resch (Eds.): Tools for High Performance Computing 2018/2019.
Springer, Cham (2021), 27-53.
Full text
2022
- (with K. Kitzing, R. Picard, S. Siegmund, S. Trostorff & M. Waurick)
A Hilbert Space Approach to Fractional Differential Equations.
J. Dyn. Differ. Equations 34 (2022), 481-504.
Full text - (with V. Kiryakova, Y. Luchko, J. A. T. Machado & V. E. Tarasov)
Trends, directions for further research, and some open problems of fractional calculus.
Nonlinear Dynam. 107 (2022), 3245-3270.
Full text - (with H. T. Tuan)
Upper and lower estimates for the separation of solutions to fractional differential equations.
Fract. Calc. Appl. Anal., 25 (2022), 166-180
Full text - A new diffusive representation for fractional derivatives, Part II: Convergence analysis of the numerical scheme.
Mathematics 10 (2022), Article No. 1245.
Full text - (with H. D. Thai & H. T. Tuan)
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems.
Fract. Calc. Appl. Anal. 25 (2022), 1324-1360.
Full text - (with S. B. Damelin)
An analytic and numerical analysis of weighted singular Cauchy integrals with exponential weights on R.
Numer. Funct. Anal. Optim. 43 (2022), 1538-1577.
Full text
2023
- A new diffusive representation for fractional derivatives, Part I: Construction, implementation and numerical examples.
In A. Cardone, M. Donatelli, F. Durastante, R. Garrappa, M. Mazza & M. Popolizio (Eds.): Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers.
Springer Nature, Singapore, 2023, pp. 1-15.
Full text - Diffusive representations for the numerical evaluation of fractional integrals.
To appear in Proc. 2023 International Conference on Fractional Differentiation and its Applications.
IEEE, Piscataway, 2023.
Full text - (with F. Uhlig)
A new approach to shooting methods for terminal value problems of fractional differential equations.
J. Sci. Comput. 97 (2023), Article No. 38.
Full text
MATLAB source code of associated software
2024
- (with R. Chaudhary & S. Hashemishahraki)
On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$.
Appl. Numer. Math. 203 (2024), 84-96.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
A constructive approach for investigating the stability of incommensurate fractional differential systems.
J. Math. Anal. Appl. 540 (2024), Article No. 128642.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
Stability properties of multi-order fractional differential systems in 3D.
IFAC PapersOnLine 58-12 (2024), 231–236.
Corrigendum: arXiv:2312.10653.
Volltext - (with R. Chaudhary)
Novel variants of diffusive representation of fractional integrals: Construction and numerical computation.
IFAC PapersOnLine 58-12 (2024), 412-417.
Volltext - (with R. Chaudhary)
Revisiting diffusive representations for enhanced numerical approximation of fractional integrals.
IFAC PapersOnLine 58-12 (2024), 418-423.
Volltext - Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives.
To appear in J. Ball, H.-O. Tylli & J. A. Virtanen (Eds.): Recent Developments in Operator
Theory, Mathematical Physics and Complex Analysis—IWOTA 2023, Helsinki. Birkhäuser, Cham.
Preprint: arXiv:2402.03487.
MATLAB source code of associated software
2025
Books
- The Analysis of Fractional Differential Equations — An application-oriented exposition using differential operators of Caputo type.
Springer, Berlin (2010), viii+247 pp., ISBN 978-3-642-14573-5. - (with D. Baleanu, E. Scalas and J. J. Trujillo)
Fractional Calculus — Models and numerical methods.
First edition, World Scientific Publ. Comp., Singapore (2012), xxiv+400 pp., ISBN 978-981-4355-20-9.
Second edition, World Scientific Publ. Comp., Singapore (2016), xxviii+448 pp., ISBN 978-981-3140-03-5. - Gemeinschaftliches Entscheiden — Untersuchung von Entscheidungsverfahren mit mathematischen Hilfsmitteln.
Springer, Berlin (2016), ix+138 pp., ISBN 978-3-662-48779-2.
(in German)
Conference Presentations
2018
- Fractional-Order Models for the Behaviour of Concrete Under Mechanical Load Over Very Long Time Intervals.
Workshop on Fractional Calculus and Applications, University of Potsdam, September 06-07, 2018 (invited plenary talk).
2019
- (a) Fractional Ordinary Differential Equations.
(b) Nonclassical Methods for the Numerical Solution of Fractional Differential Equations.
(c) Numerical Methods for Terminal Value Problems of Fractional Order.
COST Action 15225 Training School, Politecnico di Bari, Italy, July 22-26, 2019 (invited plenary talks).
2020
- Fast Computation of Fractional Integrals and its Application.
4th Conference on Numerical Methods for Fractional-Derivative Problems, Beijing Computational Science Research Center, Beijing, China, October 22-24, 2020 (invited talk; online).
2021
- Numerical Methods for Terminal Value Problems of Fractional Order.
Irish Numerical Analysis Forum, University of Limerick, Ireland, June 17, 2021 (invited talk; online). - Terminal Value Problems for Fractional Differential Equations and Their Numerical Solution.
ALOP Workshop on Nonlocal Models, University of Trier, July 12-14, 2021 (online). - Fast and Memory Efficient Solution Methods for Fractional Ordinary Differential Equations.
Joint Annual Meeting of the German Mathematicians' Union and the Austrian Mathematical Society, University of Passau, Germany, September 27 - October 01, 2021 (online). - Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
9th International Conference on Systems and Control (ICSC'2021), École Nationale Supérieure d'Ingénieurs de Caen, France, November 24-26, 2021 (online). - Stability Questions for Fractional Differential Equations.
Seminar on Dynamical Systems and Control theory, University of Würzburg, December 10, 2021 (invited talk).
2022
- Numerical Aspects of the Infinite State Representation of Fractional Differential Operators.
Computation, Analysis and Applications of PDEs with Nonlocal and Singular Operators, National University of Singapore, February 04 - March 04, 2022 (invited talk, online). - Diffusive Representations of Fractional Differential Operators and Their Use in Numerical Fractional Calculus.
Research Programme on Fractional Differential Equations, Isaac Newton Institute, University of Cambridge, UK, March 07, 2022 (invited talk, online).
2023
- Diffusive Representations for Fractional Integral Operators and Their Applications.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, February 10-11, 2023 (Poster; in German). - Diffusive Representations for the Numerical Evaluation of Fractional Integrals.
2023 International Conference on Fractional Differentiation and its Applications, Ajman University, United Arab Emirates, March 14-16, 2023 (online). - Terminal Value Problems for Fractional Ordinary Differential Equations: Analytical Properties of Their Solutions and an Efficient Numerical Algorithm.
International Workshop on Operator Theory and its Applications, Universität Helsinki, Finnland, July 31-August 04, 2023. - Efficient Handling of Fractional Order Material Laws in Finite Element Simulations.
Innovations in Fractional Calculus and Applications to Functional and Biological Materials, Centre Européen de Calcul Atomique et Moléculaire, EPF Lausanne, Switzerland, September 13-15, 2023 (invited talk). - Use of Novel Materials in the Production of Railway Sleepers.
Workshop on Sustainability, TH Würzburg-Schweinfurt and VDI, Schweinfurt, September 19,2023. - Stability Results for Multi-Order Fractional Differential Equation Systems.
International Workshop on Analysis and Numerical Approximation of Singular Problems, Peso da Régua, Portugal, 12.-14.10.2023 (invited plenary talk).
2024 - (α_1, α_2, . . . , α_n)-Eigenvalues of (n × n) Matrices: Applications, First Results, and Open Questions.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, 09.-10.02.2024 (Poster). - ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
Gauss Alliance HPC-Status Conference, TU Dresden, April 24-26, 2024. - (with S. A. Mohammadi, S. Burak, J. A. Reuter, L. Moj, K. Kassem-Manthey, B. Mohr, C. Terboven, F. Wolf & C. Woll) ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
ISC High Performance 2024, Hamburg, 12.-16.05.2024 (Poster). - Fast Numerical Algorithms for the Evaluation of Riemann-Liouville Integrals.
27th International Conference on Mathematical Modelling and Analysis, University of Tartu, Estonia, 28.-31.05.2024 (invited plenary talk). - The Approximation of Power Functions with Exponents in (-1, 0) by Sums of Exponentials and Its Applications.
Approximation Theory: Methods and Applications 2024, Università del Salento, Lecce, Italy, June 11-14, 2024 (invited plenary talk). - Efficient Algorithms for Computing Fractional Integrals.
Fractional Calculus Seminar, SISSA International School of Advanced Studies, Triest, Italy, June 28, 2024 (invited talk; online). - Diffusive Representations of Fractional Integral Operators and Their Applications.
12th International Conference on Fractional Differentiation and its Applications, Bordeaux, France, July 09-12, 2024 (plenary talk). - Integrals over R with Strongly Asymmetric Weights and Their Approximation in the Context of Numerical Solution Methods for Weakly Singular Volterra Equations.
6th Dolomites Workshop on Constructive Approximation and Applications, Alba di Canazei, Italien, 09.–13-09.2024 (invited keynote lecture). - AI-driven Design Parameter Optimization for Sheet Metal Forming Processes.
NAFEMS NORDIC Conference on AI and ML in Simulation Driven Design, Lund, Sweden, November 20–21, 2024.
Career
Biography
- 1992: Diploma in Mathematics, TU Braunschweig
- 1992-1998: Scientific Assistant, Institute of Mathematics, University of Hildesheim
(PhD in Computer Science 1994; Habilitation in Mathematics 1998) - 1998-2004: (Senior) Scientific Assistant, Department of Numerical Mathematics, TU Braunschweig
(Adjunct Professor since 2002) - 1999-2000: Temporary Professor for Numerical Mathematics, University of Gießen
- 2004-2018 Software developer and project coordinator, GNS Gesellschaft für numerische Simulation mbH, Braunschweig
- since 2018: Professor for Mathematics and Applied Computer Science, Technical University of Applied Sciences Würzburg-Schweinfurt
Additional Information
MINT-Tag Mainfranken 2021
Folien zum Vortrag "Die Mathematik der Demokratie"
Dokument(e)
MINT-Tag_Mainfranken.pdfNumerical Simulation
The team of the thematic field of numerical simulation deals with the development and implementation of reliable and efficient algorithms for the numerical treatment of innovative non-classical material laws and with the integration of such algorithms into the framework of existing general simulation software systems. The current focus of work is on memory-based material models, such as models for viscoelastic materials (polymers, biological tissue, etc.) based on differential equations of fractional order. The use of our algorithms allows users, particularly from structural mechanics and related areas, to precisely predict the behavior of the components they have designed and to optimize the design of these components.
Methods

The finite element method is an established and well-understood standard tool for simulating structural mechanical processes. In order to use the method in practice, one needs software systems that, in addition to the general mathematical framework, also incorporate the material laws of those materials that are represented in the structures to be simulated. While corresponding material algorithms exist for numerous established material classes, this is e.g. hardly the case for viscoelastic materials. An important aspect here is that proven mathematical models for such materials exhibit memory effects, i.e. the current state of deformation depends not only on the current load, but on the entire previous history. This is a significant difference to common material models which has significant software engineering implications for the algorithms to be used.
In view of this background, the Numerical Simulation team is concerned with the development and implementation of numerical methods with which such memory-based models can be treated reliably and efficiently. The current focus of work is on mathematical models based on differential equations of fractional (i.e. non-integer) order. Experience has shown that such models are particularly well suited to accurately describing the behavior of viscoelastic materials over longer periods of time. From a theoretical point of view, the so-called diffusive representation of the occurring differential and integral operators has significant advantages because, compared to traditional representations, it leads to algorithms that require less computing time, have a significantly lower memory requirement for handling the process history and can be integrated into existing, proven finite element packages with little software effort.
Projects
ProVerB
As part of the ProVerB joint project funded by the BMBF from 2018 to 2021, we developed material models for the behavior of concrete over extremely long periods of time together with the Gesellschaft für numerische Simulation mbH (Braunschweig) and the Institute for Nonlinear Mechanics at the University of Stuttgart. The background was the use of concrete as a material to produce barriers and closure systems for final storage sites for radioactive waste.
MuSiK
As part of the MuSiK joint project, which began in 2022 and is expected to run until 2025 and is also funded by the BMBF, we are once again devoting ourselves, together with the Institute for Nonlinear Mechanics at the University of Stuttgart, to the development of material models and associated numerical methods for the description of fiber-reinforced plastics and synthetic resins. The specific application here is reinforcing bars to be made from such materials for concrete in building construction and civil engineering, which are intended to serve as a replacement for the steel reinforcements previously used. Because fiber-reinforced plastics are substantially less susceptible to corrosion than structural steel, the service life of structures constructed with them can be significantly increased in this way.
Contact
Prof. Dr. Kai Diethelm
97421 Schweinfurt
* during the lecture period: Monday, 11:45-12:45, in room 1.E.41.3
* during the lecture-free period: by appointment
Supervision Informatics
Head of Scientific Computing Lab
Head, Laboratory for Scientific Computing
Ombudsperson for Good Scientific Practice

Teaching Areas
Lehrgebiete
Mathematik
Angewandte Informatik
Publications
ORCID
My ORCID-ID: 0000-0002-7276-454X
Peer-Reviewed Publications in Scientific Journals and Collections
1994-2017
For a list of my works published before my move to THWS, see here.
2018
- (with N. J. Ford)
A Note on the Well-posedness of Terminal Value Problems for Fractional Differential Equations.
J. Integral Equations Appl. 30 (2018), 371-376.
Abstract and link to full text - Numerical Methods for the Fractional Differential Equations of Viscoelasticity.
In H. Altenbach, A. Öchsner (Eds.): Encyclopedia of Continuum Mechanics. Springer, Berlin, 2018.
Abstract and link to full text
2019
- General Theory of Caputo-Type Fractional Differential Equations.
In A. Kochubei, Y. Luchko (Eds.): Handbook of Fractional Calculus with Applications, Vol. 2: Fractional Differential Equations.
De Gruyter, Berlin, 2019, pp. 1-20.
Abstract and link to full text - Fundamental Approaches for the Numerical Handling of Fractional Operators and Time-Fractional Differential Equations.
In G. E. Karniadakis (Ed.): Handbook of Fractional Calculus with Applications, Vol. 3: Numerical Methods.
De Gruyter, Berlin, 2019, pp. 1-22.
Abstract and link to full text
2020
- (with P. G. Kjeldsberg, R. Schöne, M. Gerndt, L. Riha, V. Kannan, M.-C. Sawley, J. Zapletal, A. Gocht, N. Reissmann, O. Vysocki, M. Kumaraswamy & W. E. Nagel)
Run-time Exploitation of Application Dynamism for Energy-efficient Exascale Computing.
In F. Catthoor, T. Basten, N. Zompakis, M. Geilen & P. G. Kjeldsberg (Eds.): System-Scenario-based Design Principles and Applications.
Springer International, Cham (2020), 113-126.
Abstract and link to full text - (mit R. Garrappa & M. Stynes)
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus.
Mathematics 8 (2020), Article No. 324.
Abstract
Full text (PDF) - (with R. Garrappa, A. Giusti & M. Stynes)
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used.
Fract. Calc. Appl. Anal. 23 (2020), 610-634.
Abstract and link to full text
Full text at arXiv.org
2021
- Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
In Proc. 9th International Conference on Systems and Control (ICSC 2021).
IEEE, Piscataway, 2021, pp. 455-460.
Full text - (with M. Kumaraswamy, A. Chowdhury, A. Gocht, J. Zapletal, L. Riha, M.-C. Sawley, M. Gerndt, N. Reissmann, O. Vysocky, O. Bouizi, P. G. Kjeldsberg, R. Carreras, R. Schöne, U. S. Mian, V. Kannan & W. E. Nagel)
Saving Energy Using the READEX Methodology.
In H. Mix, C. Niethammer, H. Zhou, W. E. Nagel & M. M. Resch (Eds.): Tools for High Performance Computing 2018/2019.
Springer, Cham (2021), 27-53.
Full text
2022
- (with K. Kitzing, R. Picard, S. Siegmund, S. Trostorff & M. Waurick)
A Hilbert Space Approach to Fractional Differential Equations.
J. Dyn. Differ. Equations 34 (2022), 481-504.
Full text - (with V. Kiryakova, Y. Luchko, J. A. T. Machado & V. E. Tarasov)
Trends, directions for further research, and some open problems of fractional calculus.
Nonlinear Dynam. 107 (2022), 3245-3270.
Full text - (with H. T. Tuan)
Upper and lower estimates for the separation of solutions to fractional differential equations.
Fract. Calc. Appl. Anal., 25 (2022), 166-180
Full text - A new diffusive representation for fractional derivatives, Part II: Convergence analysis of the numerical scheme.
Mathematics 10 (2022), Article No. 1245.
Full text - (with H. D. Thai & H. T. Tuan)
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems.
Fract. Calc. Appl. Anal. 25 (2022), 1324-1360.
Full text - (with S. B. Damelin)
An analytic and numerical analysis of weighted singular Cauchy integrals with exponential weights on R.
Numer. Funct. Anal. Optim. 43 (2022), 1538-1577.
Full text
2023
- A new diffusive representation for fractional derivatives, Part I: Construction, implementation and numerical examples.
In A. Cardone, M. Donatelli, F. Durastante, R. Garrappa, M. Mazza & M. Popolizio (Eds.): Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers.
Springer Nature, Singapore, 2023, pp. 1-15.
Full text - Diffusive representations for the numerical evaluation of fractional integrals.
To appear in Proc. 2023 International Conference on Fractional Differentiation and its Applications.
IEEE, Piscataway, 2023.
Full text - (with F. Uhlig)
A new approach to shooting methods for terminal value problems of fractional differential equations.
J. Sci. Comput. 97 (2023), Article No. 38.
Full text
MATLAB source code of associated software
2024
- (with R. Chaudhary & S. Hashemishahraki)
On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$.
Appl. Numer. Math. 203 (2024), 84-96.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
A constructive approach for investigating the stability of incommensurate fractional differential systems.
J. Math. Anal. Appl. 540 (2024), Article No. 128642.
Full text - (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
Stability properties of multi-order fractional differential systems in 3D.
IFAC PapersOnLine 58-12 (2024), 231–236.
Corrigendum: arXiv:2312.10653.
Volltext - (with R. Chaudhary)
Novel variants of diffusive representation of fractional integrals: Construction and numerical computation.
IFAC PapersOnLine 58-12 (2024), 412-417.
Volltext - (with R. Chaudhary)
Revisiting diffusive representations for enhanced numerical approximation of fractional integrals.
IFAC PapersOnLine 58-12 (2024), 418-423.
Volltext - Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives.
To appear in J. Ball, H.-O. Tylli & J. A. Virtanen (Eds.): Recent Developments in Operator
Theory, Mathematical Physics and Complex Analysis—IWOTA 2023, Helsinki. Birkhäuser, Cham.
Preprint: arXiv:2402.03487.
MATLAB source code of associated software
2025
Books
- The Analysis of Fractional Differential Equations — An application-oriented exposition using differential operators of Caputo type.
Springer, Berlin (2010), viii+247 pp., ISBN 978-3-642-14573-5. - (with D. Baleanu, E. Scalas and J. J. Trujillo)
Fractional Calculus — Models and numerical methods.
First edition, World Scientific Publ. Comp., Singapore (2012), xxiv+400 pp., ISBN 978-981-4355-20-9.
Second edition, World Scientific Publ. Comp., Singapore (2016), xxviii+448 pp., ISBN 978-981-3140-03-5. - Gemeinschaftliches Entscheiden — Untersuchung von Entscheidungsverfahren mit mathematischen Hilfsmitteln.
Springer, Berlin (2016), ix+138 pp., ISBN 978-3-662-48779-2.
(in German)
Conference Presentations
2018
- Fractional-Order Models for the Behaviour of Concrete Under Mechanical Load Over Very Long Time Intervals.
Workshop on Fractional Calculus and Applications, University of Potsdam, September 06-07, 2018 (invited plenary talk).
2019
- (a) Fractional Ordinary Differential Equations.
(b) Nonclassical Methods for the Numerical Solution of Fractional Differential Equations.
(c) Numerical Methods for Terminal Value Problems of Fractional Order.
COST Action 15225 Training School, Politecnico di Bari, Italy, July 22-26, 2019 (invited plenary talks).
2020
- Fast Computation of Fractional Integrals and its Application.
4th Conference on Numerical Methods for Fractional-Derivative Problems, Beijing Computational Science Research Center, Beijing, China, October 22-24, 2020 (invited talk; online).
2021
- Numerical Methods for Terminal Value Problems of Fractional Order.
Irish Numerical Analysis Forum, University of Limerick, Ireland, June 17, 2021 (invited talk; online). - Terminal Value Problems for Fractional Differential Equations and Their Numerical Solution.
ALOP Workshop on Nonlocal Models, University of Trier, July 12-14, 2021 (online). - Fast and Memory Efficient Solution Methods for Fractional Ordinary Differential Equations.
Joint Annual Meeting of the German Mathematicians' Union and the Austrian Mathematical Society, University of Passau, Germany, September 27 - October 01, 2021 (online). - Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials.
9th International Conference on Systems and Control (ICSC'2021), École Nationale Supérieure d'Ingénieurs de Caen, France, November 24-26, 2021 (online). - Stability Questions for Fractional Differential Equations.
Seminar on Dynamical Systems and Control theory, University of Würzburg, December 10, 2021 (invited talk).
2022
- Numerical Aspects of the Infinite State Representation of Fractional Differential Operators.
Computation, Analysis and Applications of PDEs with Nonlocal and Singular Operators, National University of Singapore, February 04 - March 04, 2022 (invited talk, online). - Diffusive Representations of Fractional Differential Operators and Their Use in Numerical Fractional Calculus.
Research Programme on Fractional Differential Equations, Isaac Newton Institute, University of Cambridge, UK, March 07, 2022 (invited talk, online).
2023
- Diffusive Representations for Fractional Integral Operators and Their Applications.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, February 10-11, 2023 (Poster; in German). - Diffusive Representations for the Numerical Evaluation of Fractional Integrals.
2023 International Conference on Fractional Differentiation and its Applications, Ajman University, United Arab Emirates, March 14-16, 2023 (online). - Terminal Value Problems for Fractional Ordinary Differential Equations: Analytical Properties of Their Solutions and an Efficient Numerical Algorithm.
International Workshop on Operator Theory and its Applications, Universität Helsinki, Finnland, July 31-August 04, 2023. - Efficient Handling of Fractional Order Material Laws in Finite Element Simulations.
Innovations in Fractional Calculus and Applications to Functional and Biological Materials, Centre Européen de Calcul Atomique et Moléculaire, EPF Lausanne, Switzerland, September 13-15, 2023 (invited talk). - Use of Novel Materials in the Production of Railway Sleepers.
Workshop on Sustainability, TH Würzburg-Schweinfurt and VDI, Schweinfurt, September 19,2023. - Stability Results for Multi-Order Fractional Differential Equation Systems.
International Workshop on Analysis and Numerical Approximation of Singular Problems, Peso da Régua, Portugal, 12.-14.10.2023 (invited plenary talk).
2024 - (α_1, α_2, . . . , α_n)-Eigenvalues of (n × n) Matrices: Applications, First Results, and Open Questions.
Rhein-Ruhr-Workshop über Angewandte Mathematik, Approximationstheorie und Numerische Mathematik, Bestwig, 09.-10.02.2024 (Poster). - ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
Gauss Alliance HPC-Status Conference, TU Dresden, April 24-26, 2024. - (with S. A. Mohammadi, S. Burak, J. A. Reuter, L. Moj, K. Kassem-Manthey, B. Mohr, C. Terboven, F. Wolf & C. Woll) ENSIMA - ENergy-efficient SImulation Methods for Application-oriented computational problems.
ISC High Performance 2024, Hamburg, 12.-16.05.2024 (Poster). - Fast Numerical Algorithms for the Evaluation of Riemann-Liouville Integrals.
27th International Conference on Mathematical Modelling and Analysis, University of Tartu, Estonia, 28.-31.05.2024 (invited plenary talk). - The Approximation of Power Functions with Exponents in (-1, 0) by Sums of Exponentials and Its Applications.
Approximation Theory: Methods and Applications 2024, Università del Salento, Lecce, Italy, June 11-14, 2024 (invited plenary talk). - Efficient Algorithms for Computing Fractional Integrals.
Fractional Calculus Seminar, SISSA International School of Advanced Studies, Triest, Italy, June 28, 2024 (invited talk; online). - Diffusive Representations of Fractional Integral Operators and Their Applications.
12th International Conference on Fractional Differentiation and its Applications, Bordeaux, France, July 09-12, 2024 (plenary talk). - Integrals over R with Strongly Asymmetric Weights and Their Approximation in the Context of Numerical Solution Methods for Weakly Singular Volterra Equations.
6th Dolomites Workshop on Constructive Approximation and Applications, Alba di Canazei, Italien, 09.–13-09.2024 (invited keynote lecture). - AI-driven Design Parameter Optimization for Sheet Metal Forming Processes.
NAFEMS NORDIC Conference on AI and ML in Simulation Driven Design, Lund, Sweden, November 20–21, 2024.
Career
Biography
- 1992: Diploma in Mathematics, TU Braunschweig
- 1992-1998: Scientific Assistant, Institute of Mathematics, University of Hildesheim
(PhD in Computer Science 1994; Habilitation in Mathematics 1998) - 1998-2004: (Senior) Scientific Assistant, Department of Numerical Mathematics, TU Braunschweig
(Adjunct Professor since 2002) - 1999-2000: Temporary Professor for Numerical Mathematics, University of Gießen
- 2004-2018 Software developer and project coordinator, GNS Gesellschaft für numerische Simulation mbH, Braunschweig
- since 2018: Professor for Mathematics and Applied Computer Science, Technical University of Applied Sciences Würzburg-Schweinfurt
Additional Information
MINT-Tag Mainfranken 2021
Folien zum Vortrag "Die Mathematik der Demokratie"