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

被引：1

作者：

Boutiba, Malika ^{[1
]}

Baghli-Bendimerad, Selma ^{[1
]}

Feckan, Michal ^{[2
]}

机构：

[1] Djillali Liabes Univ Sidi Bel Abbes, Math Dept, POB 89, Sidi Bel Abbes 22000, Algeria

[2] Comenius Univ, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia

来源：

ANNALES MATHEMATICAE SILESIANAE | 2023年 / 37卷 / 02期

关键词：

finite element method; partial differential equations; new fractional derivative; Lax-Milgram theorem; numerical solution; estimates; SPECTRAL METHOD; FINITE-VOLUME; APPROXIMATIONS;

D O I：

10.2478/amsil-2023-0009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：204 / 223

页数：20