ON THE PHYSICAL BEHAVIOURS OF THE CONFORMABLE FRACTIONAL MODIFIED CAMASSA– HOLM EQUATION USING TWO EFFICIENT METHODS

Abstract

In recent years, many authors have researched about fractional partial differential equations. Physical phenomena, which arise in engineering and applied science, can be defined more accurately by using FPDEs. Thus, obtaining exact solutions of the FPDEs equations have become more important to understand physical problems. In this article, we have reached the new traveling wave solutions of the conformable fractional modified Camassa – Holm equation via two efficient methods such as first integral method and the functional variable method. The wave transformation and conformable fractional derivative have been used to convert FPDE to the ordinary differential equation. The Camassa – Holm equation is physical model of shallow water waves with non-hydrostatic pressure. Thanks to these powerful methods, some comparisons, such as type of solutions and physical behaviours, have been made. Additionally, mathematica program have been used with the aim of checking of solutions. Investigating results of the fractional differential equations can help understanding complex phenomena in applied mathematics and physics.