<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Numeric Fem’s Solution for Space-Time Diffusion Partial Differential Equations with Caputo–Fabrizion and Riemann–Liouville Fractional Order’s Derivatives

Djillali Liabes University of Sidi Bel-Abbes

Department of Mathematical Analysis and Numerical Mathematics

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

Numeric Fem’s Solution for Space-Time Diffusion Partial Differential Equations with Caputo–Fabrizion and Riemann–Liouville Fractional Order’s Derivatives

Published Online: Jul 26, 2023

Page range: 204 - 223

Received: Jun 18, 2022

Accepted: Jun 09, 2023

DOI: https://doi.org/10.2478/amsil-2023-0009

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

© 2023 Malika Boutiba et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Numeric Fem’s Solution for Space-Time Diffusion Partial Differential Equations with Caputo–Fabrizion and Riemann–Liouville Fractional Order’s Derivatives

Published Online: Jul 26, 2023

Page range: 204 - 223

Received: Jun 18, 2022

Accepted: Jun 09, 2023

DOI: https://doi.org/10.2478/amsil-2023-0009

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

© 2023 Malika Boutiba et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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