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

TL;DR

This paper derives exact solutions for the space-time fractional Klein-Gordon equation with cubic nonlinearities using the solitary wave ansatz and modified Kudryashov methods, supported by computer simulations.

Contribution

It introduces novel exact solution techniques for the fractional Klein-Gordon equation with cubic nonlinearities, combining two analytical methods.

Findings

Exact soliton solutions obtained

Solutions verified through computer simulations

Enhanced understanding of fractional nonlinear wave equations

Abstract

Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this paper, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact soliton solutions are formally extacted 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.