New abundant wave solutions of the conformable space–time fractional (4+1)-dimensional Fokas equation in water waves.

A nonlinear fractional model arising in water waves theory, namely the new conformable space–time fractional (4+1)-dimensional Fokas equation, is explored via some recently developed approaches, namely, the functional variable, the generalized Kudryashov, the Jacobi elliptic function expansion and the generalized Riccati equation mapping methods. As a result, several (abundant) distinct types of new exact solutions are constructed with the aid of symbolic computation via Mathematica 9 in terms of solitary wave, periodic wave, Jacobi elliptic function and other solutions. Furthermore, some graphical representations (numerical simulations) have been provided to illuminate the physical behavior of the resultant solutions that may be very important in real world problems and applications with fractional order. [ABSTRACT FROM AUTHOR]