Solitary wave solutions to the modified nonlinear fractional Schrödinger’s equation with DPL nonlinearity

In this paper, we utilize the functional variable method to construct solitary wave (SW) solutions for the modified nonlinear fractional Schrödinger’s equation with Dual-power law nonlinearity. The fractional derivatives are considered in the truncated M-fractional sense. The functional variable method employed in this study is reliable and effective, providing exact SW and periodic wave solutions. We have examined some solutions to this equation and generated 3D, contour and 2D-polar graphics using the Maple program. We obtained SW solutions expressed by trigonometric and hyperbolic functions. To better understand their physical characteristics, we present graphical representations of our results, which include singular soliton solutions, bell-shaped SW solutions, and SW solutions of kink type. Our results demonstrate that this method is an efficacy and power approach to formulating SW solutions for nonlinear wave equations encountered in engineering and mathematical physics.