Analytical treatment for the conformable space-time fractional Benney-Luke equation via two reliable methods

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.