A new approximate analytical method and its convergence for nonlinear time-fractional partial differential equations

Abstract

The main goal of this paper is to present a new approximate analytical method called modified generalized Taylor fractional series method (MGTFSM) for solving general nonlinear time-fractional partial differential equations. The fractional derivative is considered in the Caputo sense. We establish the convergence results of the proposed method. The basic idea of the MGTFSM is to construct the solution in the form of infinite series which converges rapidly to the exact solution of the given problem. The main advantage of the proposed method compare to current methods is that method solves the nonlinear problems without using linearization, discretization, perturbation or any other restriction. The efficiency and accuracy of the MGTFSM is tested by means of different numerical examples. The results prove that the proposed method is very effective and simple for solving the nonlinear time-fractional partial differential equations problems.