A new technique for finding exact solutions of nonlinear time-fractional wave-like equations with variable coefficients

Abstract

In this paper, we give the exact solutions in terms of Mittag-Leffler functions for nonlinear time-fractional wave-like equations with variable coefficients by using a new technique, it is a combination of natural transform and variational iteration method called natural variational iteration method (NVIM). This technique enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. The numerical results shows that this method is highly effective and is practically suitable for use in these equations. Three numerical examples are given to verify the accuracy and efficiency of the proposed technique.