Homotopy perturbation method-based soliton solutions of the time-fractional (2+1)-dimensional Wu–Zhang system describing long dispersive gravity water waves in the ocean

Physical phenomena and natural disasters, such as tsunamis floods, are caused due to dispersive water waves shallow by earthquakes. In order analyze minimize damaging effects of situations, mathematical models presented different researchers. The Wu–Zhang (WZ) system is one model that describes long waves. this regard, the current study focuses on a non-linear (2 + 1)-dimensional time-fractional its importance in capturing gravity ocean. A Caputo fractional derivative WZ considered study. For solution purposes, modification homotopy perturbation method (HPM) along with Laplace transform used provide improved results terms accuracy. validity convergence, obtained compared differential (FDTM), modified variational iteration (mVIM), Adomian decomposition (mADM). Analysis indicates effectiveness proposed methodology. Furthermore, effect parameters given analyzed numerically graphically at both integral orders. Moreover, Caputo, Caputo–Fabrizio, Atangana–Baleanu approaches derivatives applied affirms algorithm reliable tool can be higher dimensional systems science engineering.