An accurate spectral Galerkin method for solving multiterm fractional differential equations
type: Item
instance of: scholarly article
title: An accurate spectral Galerkin method for solving multiterm fractional differential equations
zbMATH Open document ID: 1407.65081
DOI: 10.1155/2014/728736
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper reports a new formula expressing the Caputo fractional derivatives for any order of shifted generalized Jacobi polynomials of any degree in terms of shifted generalized Jacobi polynomials themselves. A direct solution technique is presented for solving multiterm fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using spectral shifted generalized Jacobi Galerkin method. The homogeneous initial conditions are satisfied exactly by using a class of shifted generalized Jacobi polynomials as a polynomial basis of the truncated expansion for the approximate solution. The approximation of the spatial Caputo fractional order derivatives is expanded in terms of a class of shifted generalized Jacobi polynomials \(J_n^{\alpha, - \beta}(x)\) with \(x \in(0, 1)\), and \(n\) is the polynomial degree. Several numerical examples with comparisons with the exact solutions are given to confirm the reliability of the proposed method for multiterm FDEs.
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7017136
Wikidata QID: Q59071725
author: A. H. Bhrawy
author: A. S. Alofi
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/728736
OpenAlex ID: W2127363112
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description: scientific article; zbMATH DE number 7017136