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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.
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
26A33Fractional derivatives and integrals (real functions)
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
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