Solving systems of fractional differential equations using differential transform method

Ertürk V. S., Momani S.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.215, no.1, pp.142-151, 2008 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 215 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.1016/j.cam.2007.03.029
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.142-151
  • Keywords: differential transform method, fractional differential equation, Caputo fractional derivative, numerical solutions, APPROXIMATE SOLUTIONS
  • Ondokuz Mayıs University Affiliated: No

Abstract

This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations. (C) 2007 Elsevier B.V. All rights reserved.