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New analytical method for solving nonlinear time-fractional reaction-diffusion-convection problems. (English) Zbl 1467.35337

This paper proposes a new analytical method called generalized Taylor fractional series method (GTFSM) for solving nonlinear time-fractional reaction-diffusion-convection initial value problems. The advantage of the proposed method compared with the existing methods is, that method solves the nonlinear problems without using linearization and any other restriction. The accuracy and efficiency of the method is tested by means of two numerical examples. Obtained results show that the proposed method is very effective and simple for solving different types of nonlinear fractional problems.

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35K57 Reaction-diffusion equations
35A35 Theoretical approximation in context of PDEs
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