A new approach for space-time fractional partial differential equations by residual power series method

Bayrak M. A., Demir A.

APPLIED MATHEMATICS AND COMPUTATION, vol.336, pp.215-230, 2018 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 336
  • Publication Date: 2018
  • Doi Number: 10.1016/j.amc.2018.04.032
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.215-230
  • Keywords: Residual power series method, Space-time fractional partial differential equations, Caputo derivative
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, the approximate analytic solution of any order space-time fractional differential equations is constructed by means of semi-analytical method, named as residual power series method (RPSM). The first step is to reduce space-time fractional differential equation to either a space fractional differential equations or a time fractional differential equations before applying RSPM. The main step is to obtain fractional power series solutions by RSPM. At the final step, it is shown that RPSM is very efficacious, plain and powerful for obtaining the solution of any-order space-time fractional differential equations in the form of fractional power series by illustrative examples. (C) 2018 Elsevier Inc. All rights reserved.