New analytic solutions of the space-time fractional Broer–Kaup and approximate long water wave equations

摘要

In the present paper, theexp(??(ξ))expansion method is applied to the fractional Broer–Kaup and approximate long water wave equations. The explicit approximate traveling wave solutions are obtained by using this method. Here, fractional derivatives are defined in the conformable sense. The obtained traveling wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Simulations of the obtained solutions are given at the end of the paper.