Prof. Dr. Kai Diethelm

Lehrgebiete

Mathematik

Angewandte Informatik

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
• (with S. Hashemishahraki, H. D. Thai & H. T. Tuan)
  Stability properties of multi-order fractional differential systems in 3D.
  Submitted for publication; preprint: arXiv:2312.10653
• (with R. Chaudhary)
  Novel variants of diffusive representation of fractional integrals: Construction and numerical computation.
  Submitted for publication; preprint: arXiv:2312.11305.
• (with R. Chaudhary)
  Revisiting diffusive representations for enhanced numerical approximation of fractional integrals.
  Submitted for publication; preprint: arXiv:2312.11590.
  
  

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
  
• Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $\alpha \in (1,2)$ With Caputo Derivatives.
  Submitted for publication; preprint: arXiv:2402.03487.
  MATLAB source code of associated software
• (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
  

Books

1. 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.
2. (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.
3. 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).
  

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
  

MINT-Tag Mainfranken 2021

Folien zum Vortrag "Die Mathematik der Demokratie"

Dokument(e)

• Scientific Computing Laboratory