A Galerkin finite element method for the space Hadamard fractional partial differential equation

Zhengang Zhao and Yunying Zheng

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 214, issue C, 272-289

Abstract: In this paper, we study the Galerkin finite element approximation for the space Hadamard fractional partial differential equation. We first introduce a modified Fourier transform to analyse the Hadamard fractional calculus, construct the fractional derivative spaces and fractional Sobolev space. Furthermore, we investigate the existence and uniqueness of the weak solution in the fractional Sobolev space. Then using a newly defined log-Lagrangian polynomial as shape function, we discuss the convergence analysis of the semi-discrete scheme. Together with the Crank–Nicolson scheme in time, we present a fully discrete scheme, analyse the stability and convergence. Finally a numerical example is displayed which support the theoretical analysis.

Keywords: Hadamard fractional derivative; Hadamard fractional differential equation; Hadamard fractional derivative space; Galerkin finite element method (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:214:y:2023:i:c:p:272-289

DOI: 10.1016/j.matcom.2023.06.022

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