Analysis of traveling wave solutions of two space-time nonlinear fractional differential equations by the first-integral method

The intent of this work to implement first-integral method to study traveling wave solutions of some space-time nonlinear fractional differential equations (FDEs) and present their graphical simulations for analyzing different wave profiles. We show how a specific properties of Gamma functions and wave transformation can be used to reduce a FDE to an ordinary one. This method works well and reveals distinct exact solutions which are classified into two different types, namely trigonometric function and hyperbolic function solutions. The results are also depicted graphically in both 3D and 2D for different values of associated parameters. The obtained results may be useful to understand ion-acoustic waves in plasma, shallow water waves in seas and the evolution of a wave packet in three dimensions with finite depth on water under weak nonlinearity by the space-time-fractional regularized long wave equation and space-time-fractional Davey-Stewartson equation, respectively.