Novel optical solitons to the perturbed Gerdjikov–Ivanov equation with truncated M-fractional conformable derivative

Abstract

The generalized Riccati equation (GRE) together with the basic simplest equation method (SEM) is investigated to deal with the nonlinear fractional differential equations. This method contains the auxiliary equation φ′(η) = Δφ(η)2 + λφ(η) + Ω with arbitrary non-variable coefficients that gives a variety of soliton solutions. Here, we apply this technique to obtain novel optical solitons solutions for the perturbed Gerdjikov–Ivanov (PGI) equation with truncated M-fractional derivative. 3D and contour plot diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences.