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Solutions of a fractional oscillator by using differential transform method. (English) Zbl 1189.34068

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:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
45J05 Integro-ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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