New Traveling Wave Solutions for Space-Time Fractional Modified Equal Width Equation with Beta Derivative

This work is based on finding the new and interesting travelling wave solutions of space-time fractional modified equal width equation, which is a pulse-like solitary wave nonlinear wave equation with cubic nonlinearity. The most efficient and reliable methodology, the unified method has been used coupled with the beta derivative to get the required results. This approach allows one to discover solutions to nonlinear evolution equations in polynomial and rational forms. All of the developed solutions are consistent with the requirements. Also, the obtained solutions are displayed on 3D and 2D graphs to represent the physical meaning of constructed solutions graphically. The findings show that the applied method is useful and can be used to solve other fractional non-linear evolution equations raised in natural and applied sciences