Influence of fractional time order on W-shaped and Modulation Instability gain in fractional Nonlinear Schrodinger Equation

In this paper, we study the influence of fractional time derivative on W-shaped profile and Modulation Instability gain in fractional Nonlinear Schrodinger Equation (NLSE) which could be used to describe the propagation of pulses in random media, optical metamaterials and others nonlinear systems. We first imply the auxiliary equation method to set up bright, dark and W-shape optical solitons solutions under certain conditions. Thereafter, we graphically depict the obtained results which deeply show the potency of the fractional parameter order on the width and shape of the solitons. We then study the Modulation Instability (MI) gain spectra and we end up remarking that the MI gain sidebands and the MI gain shapes are mainly influenced by the fractional time derivative parameter compared to the previous works reported in nonlinear optic fibers (Wyller et al., 2002; Zhanga et al., 2017).