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Zbl 1221.34022
Erturk, Vedat Suat; Momani, Shaher; Odibat, Zaid
Application of generalized differential transform method to multi-order fractional differential equations. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 13, No. 8, 1642-1654 (2008). ISSN 1007-5704

Summary: In a recent paper [Appl. Math. Comput. 197, No. 2, 467--477 (2008; Zbl 1141.65092)] the authors presented a new generalization of the differential transform method that extend 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 $y^{(\mu )}(t)=f(t,y(t),y^{(\beta_{1})}(t),y^{(\beta_{2})}(t),\ldots ,y^{(\beta_{n})}(t))$ with $\mu >\beta _{n}>\beta _{n-1}>\ldots >\beta _{1}>0$, 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.

MSC 2000:: *34A12 Initial value problems for ODE
34A08
34A25 Analytical theory of ODE

Keywords: fractional differential equations; differential transform method; multi-order equations; Caputo fractional derivative

Citations: Zbl 1141.65092

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