Traveling wave solutions for space-time fractional Cahn Hilliard equation and space-time fractional symmetric regularized long-wave equation

Abstract

Over the last few years, a direct method known as the new auxiliary method has been shown to solve non-linear partial differential equations effectively where this method can give more exact solutions compared to the traditional direct methods. Due to these promising results, efforts are now being made to extend this method in solving the more complicated non-linear fractional partial differential equations. The new auxiliary method is a very powerful, felicitous, and effective method to get exact and traveling wave solutions of partial differential equations. Therefore, we apply the new auxiliary method to solve for the traveling wave solutions of the space-time fractional Cahn-Hilliard equation and the space-time fractional symmetric regularized long-wave equation. Furthermore, it is considered as more general method for solving that time of equations because it is shown that more exact solutions for the traveling wave on these equations will be obtained with the application of the new auxiliary method.

Keywords

• The new auxiliary method
• Conformable derivative
• Exact solution
• Space-time fractional Cahn-Hilliard equation
• Space-time fractional symmetric regularized long-wave equation