On dynamical behavior for approximate solutions sustained by nonlinear fractional damped Burger and Sharma–Tasso–Olver equation

Abstract

In this paper, we study a nonlinear fractional Damped Burger and Sharma–Tasso–Olver equation using a new novel technique, called homotopy perturbation transform method (FHPTM). There are three examples used to demonstrate and validate the proposed algorithm’s efficiency. This nonlinear model depicts nonlinear wave processes in fluid dynamics, ecology, solid-state physics, shallow-water wave propagation, optical fibers, fluid mechanics, plasma physics, and other applied science, engineering, and mathematical physics disciplines, as well as other phenomena. Numerous algebraic properties of the fractional derivative Caputo–Fabrizio operator are illustrated concerning the Laplace transformation to demonstrate their utility. Different graphs and tables compare the results obtained by R. Nawaz et al. [Alex. Eng. J. 60, 3205 (2021)] and M. S. Rawashdeh [Appl. Math. Inform. Sci. 9, 1239 (2015)]. The proposed scheme accelerates the convergence of the series solution and guarantees the convergence associated with the homotopy parameter. Furthermore, the physical nature of various fractional orders has been captured in plots. The obtained results demonstrate that the employed solution procedure is dependable and methodical in investigating the behaviors of nonlinear models of both integer and fractional orders.