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Analytical approximate solutions of the fractional convection-diffusion equation with nonlinear source term by He’s homotopy perturbation method. (English) Zbl 1192.65137
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 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:
65M70Spectral, collocation and related methods (IVP of PDE)
26A33Fractional derivatives and integrals (real functions)
35R11Fractional partial differential equations
35K55Nonlinear parabolic equations
35C10Series solutions of PDE