Generalized differential transform method: Application to differential equations of fractional order

Odibat Z., Momani S., Ertürk V. S.

APPLIED MATHEMATICS AND COMPUTATION, vol.197, no.2, pp.467-477, 2008 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 197 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1016/j.amc.2007.07.068
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.467-477
  • Keywords: differential transform method, generalized Taylor formula, Caputo fractional derivative
  • Ondokuz Mayıs University Affiliated: No

Abstract

In this paper we propose a new generalization of the one-dimensional differential transform method that will extend the application of the method to differential equations of fractional order. The new generalization is based on generalized Taylor's formula and Caputo fractional derivative. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives. (c) 2007 Elsevier Inc. All rights reserved.