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 - Qayyum, Mubashir; Ahmad, Efaza; Tauseef Saeed, Syed; Ahmad, Hijaz; Askar, Sameh (Frontiers in Physics, 2023)
Physical phenomena and natural disasters such as tsunamis and floods are due to dispersive water waves and shallow waves caused by earthquakes. In order to analyze and minimize damaging effects of such situations, mathematical models are presented by different researchers. Wu-Zhang (WZ) system is one of such models which describes long dispersive waves. In this regard, current study focuses on a non-linear (2 + 1)-dimensional time-fractional Wu–Zhang (WZ) system due to its importance in capturing long dispersive gravity water waves in ocean. Fractional derivative in WZ system is considered in Caputo sense. For solution purposes, modification of homotopy perturbation method (HPM) along with Laplace transform is used to provide improved results in terms of accuracy. Results are compared with the modified Adomian decomposition method (mADM), fractional differential transform method (FDTM) and modified variational iteration method (mVIM) for validity and convergence. Analysis of results indicate the effectiveness of the proposed methodology. Furthermore, effect of fractional parameter on the given model is analyzed through numerically and graphically at both integral and fractional orders. Moreover, Caputo, Caputo-Fabrizio and Atangana–Baleanu approaches of fractional derivatives are applied and compared graphically in the current study. Analysis affirm that proposed algorithm is a reliable tool and can be used for higher dimensional fractional systems in science and engineering.