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Zbl 1189.34068
Al-Rabtah, Adel; Ertürk, Vedat Suat; Momani, Shaher
Solutions of a fractional oscillator by using differential transform method. (English)
[J] Comput. Math. Appl. 59, No. 3, 1356-1362 (2010). ISSN 0898-1221

Summary: We present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. 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 proposed method.

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
26A33 Fractional derivatives and integrals (real functions)
34A08
45J05 Integro-ordinary differential equations
65L05 Initial value problems for ODE (numerical methods)

Keywords: differential transform method; fractional oscillator; fractional differential equation; Caputo fractional derivative; numerical solutions

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Zentralblatt MATH Berlin [Germany]