Generalized differential transform method for solving a space-and time-fractional diffusion-wave equation

Momani S., Odibat Z., Erturk V. S.

PHYSICS LETTERS A, vol.370, no.5-6, pp.379-387, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 370 Issue: 5-6
  • Publication Date: 2007
  • Doi Number: 10.1016/j.physleta.2007.05.083
  • Journal Name: PHYSICS LETTERS A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.379-387
  • Keywords: differential transform method, generalized Taylor formula, fractional differential equations, diffusion-wave equation, BOUNDARY-VALUE-PROBLEMS, DECOMPOSITION METHOD
  • Ondokuz Mayıs University Affiliated: No

Abstract

In this Letter we propose a new generalization of the two-dimensional differential transform method that will extend the application of the method to a diffusion-wave equation with space- and time-fractional derivatives. The new generalization is based on generalized Taylor's formula and Caputo fractional derivative. Theorems that are never existed before are introduced with their proofs. Several illustrative examples are given to demonstrate the effectiveness of the obtained results. The results reveal that the technique introduced here is very effective and convenient for solving partial differential equations of fractional order. (C) 2007 Elsevier B.V. All rights reserved.