New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations

Abstract

In this paper, the authors discussed the new wave solutions of time-space fractional Liouville andSine-Gordon equations by using a reliable analytical method called sub-equation method. The fractional derivativesof considered equations are handled in conformable sense. Conformable derivative which is an easy and applicabletype of fractional derivative, satisfies basic properties of known derivative with integer order such as Leibnizrule, quotient rule, chain rule. These properties of conformable derivative superior to other popular definitions onobtaining analytical solutions of fractional equations.