Numeric FEM's solution for space-time diffusion partial dfferential equations with Caputo–Fabrizion and Riemann–Liouville fractional order's derivatives

Malika Boutiba; Selma Baghli-Bendimerad; Michal Fečkan

Published: 2023-07-26

Vol. 37 No. 2 (2023)

Numeric FEM's solution for space-time diffusion partial dfferential equations with Caputo–Fabrizion and Riemann–Liouville fractional order's derivatives

Malika Boutiba , Selma Baghli-Bendimerad

, Michal Fečkan

Abstract

In this paper, we use the finite element method to solve the fractional space-time diffusion equation over finite fields. This equation is obtained from the standard diffusion equation by replacing the first temporal derivative with the new fractional derivative recently introduced by Caputo and Fabrizion and the second spatial derivative with the Riemann–Liouville fractional derivative. The existence and uniqueness of the numerical solution and the result of error estimation are given. Numerical examples are used to support the theoretical results.

Keywords:

finite element method , partial differential equations , new fractional derivative , Lax–Milgram theorem , numerical solution , estimates

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Boutiba, M., Baghli-Bendimerad, S., & Fečkan, M. (2023). Numeric FEM’s solution for space-time diffusion partial dfferential equations with Caputo–Fabrizion and Riemann–Liouville fractional order’s derivatives. Annales Mathematicae Silesianae, 37(2), 204–223. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15789

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Malika Boutiba

Affiliation:

Mathematics Department, Djillali Liabes University of Sidi Bel-Abbes Algeria

Selma Baghli-Bendimerad

selmabaghli@gmail.com
https://orcid.org/0000-0003-4397-8300

Affiliation:

Mathematics Department, Djillali Liabes University of Sidi Bel-Abbes Algeria

Michal Fečkan

Affiliation:

Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava Slovakia

Vol. 37 No. 2 (2023)
Published: 2023-09-21

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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