EXACT SOLITARY WAVE SOLUTIONS TO THE FRACTIONAL GERDJIKOV-IVANOV EQUATION WITH CONFORMABLE DERIVATIVE

Abstract

Searching for exact analytic solutions to the partial di erential equations is one of the most challenging problems in mathematical physics. The main contribution in this paper is to consider the fractional Gerdjikov-Ivanov equation with conformable derivative, and obtaining new exact solitary solutions with the aid of conformable deriva- tive and Kudryashov method. Then, we get new soliton solutions for fGI equation. This equation plays a signi cant role in non-linear ber optics. It also has many important applications in photonic crystal bers. To this end, rstly, we obtain some novel opti- cal solutions of the equation via a newly proposed analytical method called generalized exponential rational function method. In order to understand the dynamic behavior of these solutions, several graphs are plotted. To the best of our knowledge, these two techniques have never been tested for the equation in the literature. The ndings of this article may have a high signi cance application while handling the other non-linear PDEs.