Title: A semi-analytical method for solving a class of non-homogeneous time-fractional partial differential equations

Authors: Jianke Zhang; Luyang Yin

Addresses: School of Science, Xi'an University of Posts and Telecommunications, Xi'an, China ' School of Science, Xi'an University of Posts and Telecommunications, Xi'an, China

Abstract: In this paper, a new kind of hybrid method is established to get the analytical approximate solutions for a class of non-homogeneous time-fractional partial differential equations. This hybrid method is with respect to the fourier series and the Chelyshkov polynomials. Firstly, the Fourier series is presented to transform the time-fractional partial differential equations to the time-fractional ordinary differential equations. Secondly, the operational matrix based on Chelyshkov polynomials is proposed to attain the analytical approximate solutions with the polynomial least squares method. The fractional derivatives are in Caputo sense. Several numerical examples are given in this paper, whose results are shown in the form of graphs and data. The results show that this hybrid method is effective to solve this class of non-homogeneous time-fractional partial differential equations.

Keywords: Fourier series; Chelyshkov polynomials; Caputo fractional derivative.

DOI: 10.1504/IJCSM.2021.117601

International Journal of Computing Science and Mathematics, 2021 Vol.13 No.4, pp.391 - 400

Received: 18 Mar 2019
Accepted: 14 Apr 2020
Published online: 15 Sep 2021 *

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