Application of the modified simple equation method for solving two nonlinear time-fractional long water wave

Recently, nonlinear fractional partial differential equations have been used to model many phenomena in applied sciences and engineering. In this study, the modified simple equation scheme is implemented to obtain some new traveling wave solutions of the nonlinear conformable time-fractional approximate long water wave equation and the nonlinear conformable coupled time-fractional Boussinesq-Burger equation, which are used in the expression of shallow-water waves. The time-fractional derivatives are described in terms of conformable fractional derivative sense. Consequently, new exact traveling wave solutions of both equations are achieved.