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Zbl 1192.65137
Momani, Shaher; Y ild ir im, Ahmet
Analytical approximate solutions of the fractional convection-diffusion equation with nonlinear source term by He's homotopy perturbation method. (English)
[J] Int. J. Comput. Math. 87, No. 5, 1057-1065 (2010). ISSN 0020-7160; ISSN 1029-0265/e

Summary: We present a framework to obtain analytical approximate solutions to a nonlinear fractional convection-diffusion equation. The fractional derivative is considered in the Caputo sense. The applications of {\it J. He}'s homotopy perturbation method [Comput. Methods Appl. Mech. Eng. 178, No.~3--4, 257--262 (1999; Zbl 0956.70017)] are extended to derive analytical solutions in the form of a series with easily computed terms for this equation. Some examples are tested and the results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations of fractional order.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
26A33 Fractional derivatives and integrals (real functions)
35R11
35K55 Nonlinear parabolic equations
35C10 Series solutions of PDE

Keywords: homotopy perturbation method; Caputo fractional derivative; series solution; numerical examples; nonlinear fractional convection-diffusion equation

Citations: Zbl 0956.70017

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