Abundant M-Fractional Optical Solitons to the Pertubed Gerdjikov-Ivanov Equation Treating the Mathematical Nonlinear Optics

Abstract In this paper, the perturbed Gerdjikov-Ivanov (GI) equation using a truncated Mfractional derivative is studied in mathematical nonlinear optics. We explore its novel dark and other soliton solutions and compared them with the existing results. To obtain the objective, two particular methods, modified extended tanh expansion method and Expa function method, are implemented. In this exert, a arrangement of exact solitons are received as well as verified by utilizing the MATHEMATICA software. The dynamical characteristics of the obtained results, along with a fractional parameter, are also discussed via two and three-dimensional graphs. These solutions suggest that the employed methods are impressive, determined and smooth as compared to many other methods. The work of this paper is of high importance regarding its applications in photonic crystal fibers and mathematical physics.