Investigation of New Optical Solutions of the Fractional Schrodinger Equation With Accounting for Third-Order Nonlinearity

In this paper, we consider the quadratic-cubic nonlinear Schrdinger equation (QC-NLSE) formulated with the M-truncated derivative (MTD).By employing the F-expansion method, a variety of exact analytical solutions are obtained, including periodic, bright, kink, anti-kink, singular, and dark soliton structures.The method is shown to be systematic and effective for constructing exact solutions of nonlinear evolution equations with fractional-order characteristics.The main contribution of this work is the derivation and classification of a diverse family of wave solutions to the QC-NLSE using MTD.Graphical simulations are performed using MATLAB to illustrate the influence of the fractional parameter on the behavior of the obtained solutions.The results demonstrate that variations in this parameter lead to noticeable changes in the shape and propagation characteristics of the wave structures, while the analytical method serves to describe these properties.