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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

Int. J. Comput. Math. 87, No. 5, 1057-1065 (2010); correction ibid. 98, No. 6, 1291 (2021).
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:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
35K55 Nonlinear parabolic equations
35C10 Series solutions to PDEs

Citations:

Zbl 0956.70017
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References:

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