Work

Galerkin Finite Element Method for Caputo–Hadamard Time-Space Fractional Diffusion Equation

Year: 2024

Type: article

Abstract: In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately. We first use the Laplace transform and the modified Fourier transform to study the analytical solution of the Cauchy problem. Then, using the Galerkin finite element method in space, we generate a semi-discrete scheme and study the convergence analysis. Furthermore, using the L1 scheme of the Caputo derivative in time, we construct a fully discrete scheme and then discuss the stability and error estimation in detail. Finally, the numerical experiments are displaced to verify the theoretical results.

Source: Mathematics

DOI: 10.3390/math12233786

Authors: Zhengang Zhao, Yunying Zheng

Institutions: Shanghai Customs College, Huaibei Normal University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Natural Science Foundation of Shanghai, Natural Science Foundation of Anhui Province