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

The main objective of this paper is to present a new approximate analytical method called Modied Generalized Taylor Fractional Series Method (MGTFSM) for solving general nonlinear time-fractional partial dierential equations. The fractional derivative is considered in the Caputo sense. The convergence results of the proposed method are established here. The basic idea of the MGTFSM is to construct the solution in the form of innite series that converges rapidly to the exact solution of the given problem. The main advantage of the proposed method, compared to current methods, is that the method solves the nonlinear problems without using linearization, discretization, perturbation, or any other restriction. The eciency and accuracy of the MGTFSM are 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.