Abstract

KHALOUTA, Ali  and  KADEM, Abdelouahab. New analytical method for solving nonlinear time-fractional reaction-diffusion-convection problems. Rev.colomb.mat. [online]. 2020, vol.54, n.1, pp.1-11. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n1.89771.

In this paper, we propose a new analytical method called generalized Taylor fractional series method (GTFSM) for solving nonlinear timefractional reaction-diffusion-convection initial value problems. Our obtained results are given in the form of a new theorem. 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 interpret that the proposed method is very effective and simple for solving different types of nonlinear fractional problems.

Keywords : Nonlinear time-fractional reaction-diffusion-convection problems; Caputo fractional derivative; generalized Taylor fractional series method.

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