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Application of homotopy-perturbation method to fractional IVPs. (English) Zbl 1142.65104
Summary: Fractional initial-value problems (fIVPs) arise from many fields of physics and play a very important role in various branches of science and engineering. Finding accurate and efficient methods for solving fIVPs has become an active research undertaking. In this paper, both linear and nonlinear fIVPs are considered. Exact and/or approximate analytical solutions of the fIVPs are obtained by the analytic homotopy-perturbation method (HPM). The results of applying this procedure to the studied cases show the high accuracy, simplicity and efficiency of the approach.

MSC:
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
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