Numeric FEM's solution for space-time diffusion partial dfferential equations with Caputo–Fabrizion and Riemann–Liouville fractional order's derivatives
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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Mathematics Department, Djillali Liabes University of Sidi Bel-Abbes Algeria
Mathematics Department, Djillali Liabes University of Sidi Bel-Abbes Algeria
https://orcid.org/0000-0003-4397-8300
Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava Slovakia
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