Exact solitary wave solutions to the fractional Gerdjikov-Ivanov equation with conformable derivative

Abstract

Searching for exact analytic solutions to the partial differential 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 derivative and Kudryashov method. Then, we get new soliton solutions for fGI equation. This equation plays a significant role in non-linear fiber optics. It also has many important applications in photonic crystal fibers. To this end, firstly, we obtain some novel optical 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 findings of this article may have a high significance application while handling the other non-linear PDEs.