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doi:10.1016/j.cnsns.2007.02.006 
Copyright © 2007 Elsevier B.V. All rights reserved.
Application of generalized differential transform method to multi-order fractional differential equations
Received 19 January 2007;
| Referred to by: | | Comments on “Application of generalized differential transform method to multi-order fractional differential equations”, Vedat Suat Erturk, Shaher Momani, Zaid Odibat [Commun Nonlinear Sci Numer Simul 2008;13:1642–54] Communications in Nonlinear Science and Numerical Simulation, Volume 13, Issue 8, October 2008, Pages 1737-1740 Aytac Arikoglu, Ibrahim Ozkol  PDF (107 K)
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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(μ)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with μ>βn>βn-1>…>β1>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.
Keywords: Fractional differential equations; Differential transform method; Multi-order equations; Caputo fractional derivative
PACS classification codes: 02.30.Lt; 02.30.−f; 02.30.Gp; 02.30.Hq; 02.60.−x
