An efficient semi-analytical method for solving the generalized regularized long wave equations with a new fractional derivative operator

Abstract

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to the generalized regularized long wave equations with a new fractional operator to obtain new approximate solutions. We transform the classical generalized regularized long wave equations to fractional differential form by using the Atangana-Baleanu fractional derivative which is defined with the Mittag-Leffler function. To show the efficiency of the proposed method, a numerical example is given for different values of physical parameters.