Application of generalized differential transform method to multi-order fractional differential equations

Ertürk V. S., Momani S., Odibat Z.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.13, no.8, pp.1642-1654, 2008 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 8
  • Publication Date: 2008
  • Doi Number: 10.1016/j.cnsns.2007.02.006
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1642-1654
  • Keywords: fractional differential equations, differential transform method, multi-order equations, caputo fractional derivative, NUMERICAL-SOLUTION, CALCULUS, SYSTEMS
  • Ondokuz Mayıs University Affiliated: No

Abstract

In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl. Math Comput. submitted for publication] the authors presented a new generalization of the differential transform method that would extended the application of the method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y((mu))(t) = f (t, y(t), y((beta 1))(t), y((beta 2)) (t),..., y((beta n))(t)) with mu > beta(n) > beta(n-1) >...> beta(1) > 0, combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization. (c) 2007 Elsevier B.V. All rights reserved.