Describing Water Wave Propagation Using the (Fomrula Presented.)Expansion Method

In the present study, our focus is to obtain the different analytical solutions to the space–time fractional Bogoyavlenskii equation in the sense of the Jumaries-modified Riemann–Liouville derivative and to the conformable time–fractional-modified nonlinear Schrödinger equation that describes the fluctuation of sea waves and the propagation of water waves in ocean engineering, respectively. The (Formula presented.) –expansion method is applied to investigate the dynamics of solitons in relation to governing models. Moreover, the restriction conditions for the existence of solutions are reported. In addition, we note that the accomplished solutions are useful to the description of wave fluctuation and the wave propagation survey and are also significant for experimental and numerical verification in ocean engineering.