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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:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
45J05Integro-ordinary differential equations
65L05Initial value problems for ODE (numerical methods)
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