A New Iterative Natural Transform Method for Solving Nonlinear Caputo Time-Fractional Partial Differential Equations

Abstract

The main purpose of this paper is to present the solutions of a class of nonlinear Caputo time-fractional partial differential equations, in particular nonlin ear Caputo time-fractional wave-like equations with variable coefficients in terms of Mittag-Leffler functions by using new technique called, new iterative natural transform method (NINTM). This method introduced an efficient tool for solving
these class of equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed method. The results obtained show that the method described by NINTM is a very simple and easy method compared to the other methods and gives the approximate solution in the form of infinite series, this series in closed form gives the corresponding exact solution of the given problem.

Key words and phrases. Nonlinear Caputo time-fractional wave-like equations, Caputo fractional derivative, natural transform, new iterative method.

2010 Mathematics Subject Classification. Primary 35R11, 26A33; Secondary 83C15, 74G10