The fractional partial differential equations have wide applications in science and engineering. In this paper, the Kudryashov techniques were utilized to obtain an exact solution of both fractional generalized equal width (GEW)-Burgers and classical GEW-Burgers equations. The general analytical solutions of the two partial differential equations are constructed for n>1. The graphical representation of the solutions is given in comparison with some previous results in the literature. The advantages and disadvantages of the method were listed.

In this study, with help of the Mathematica software, we employ the Kudryashov method and the modified extended tanh expansion method with the Riccati differential equation to analytically treat the Benney-Luke equation. The Benney-Luke equation considered in this study features fractional derivatives in both the spatial and the temporal variables of the newly introduced conformable fractional derivative. We extensively examine the equation via the two methods, and we construct various structures such as the exponential functions, trigonometric functions and hyperbolic functions. Finally, we depict the graphs of all solutions.