Title: A study on spectral methods for linear and nonlinear fractional differential equations

Authors: Mahmoud Behroozifar; Farkhondeh Ahmadpour

Addresses: Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, P.O. Box 47148-71167, Babol, Mazandaran, Iran ' Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, P.O. Box 47148-71167, Babol, Mazandaran, Iran

Abstract: In this paper, a computational method based on the spectral methods with shifted Jacobi polynomials is applied for the numerical solution of the linear and nonlinear multi-order fractional differential equations. Fractional derivative is described in the Caputo sense. Operational matrix of fractional differential of shifted Jacobi polynomials is stated. This matrix together with the tau method and collocation method are utilised to reduce the linear and nonlinear fractional differential equations to a system of algebraic equations, respectively. The purpose of this paper is to make a comparison between this simple method and other existing methods to show the performance and preciseness of the presented method. Due to this, we used this technique for some illustrative numerical tests which the results demonstrate the validity and efficiency of the method.

Keywords: fractional-order differential equation; operational matrix; Jacobi polynomials; spectral method; Caputo derivative.

DOI: 10.1504/IJCSM.2019.104023

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.6, pp.545 - 556

Received: 12 Apr 2017
Accepted: 14 Aug 2017

Published online: 05 Dec 2019 *

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