Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised Pochhammer-Chree equation in mathematical physics

Abstract

In this Paper, fractional homotopy perturbation transform method (FHPTM) is used to obtain a variety of approximate solutions for the nonlinear fractional generalized Pochhammer-Chree equation which describes certain interesting higher-dimensional waves in harmonic studies, electrical, fluid mechanics, and other fields. By apply the caputo fabrizio derivative via laplace transform technique, we investigate all concerned wave models that have been used in the examination for the propagation of harmonic waves in a cylindrical rod and several problems in fluid mechanics and wave theory in physics. Banach’s fixed point hypothesis is tested for governing fractional-order model in order to establish the existence and uniqueness of the achieved solution. We considered the model in terms of arbitrary order with three cases and introduced corresponding numerical simulations to demonstrate and validate the effectiveness of the proposed algorithm. By assigning appropriate values to free parameters, dynamical wave structures of some approximate solutions are graphically demonstrated using 2D and 3D fig. This method can also be used to approximate the solutions of other well-known equations in engineering physics, quantum field , and other applied sciences. Furthermore, various simulations are used to demonstrate the physical behaviors of the acquired solution with respect to fractional integer order.