Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods

Abstract

Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this work, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact soliton solutions are formally extracted by using the solitary wave ansatz method. Some solutions are also illustrated by the computer simulations. Besides, the modified Kudryashov method is used to construct exact solutions of this equation.