Equations (FSEs) using Caputo fractional derivatives. The Schrödinger Equation is a fundamental paradigm for understanding complex nonlinear systems, including hydrodynamics, quantum condensates, nonlinear optics, and shallow-water waves. We employ the innovative Formula: see text- expansion technique to tackle the FSE system. By applying a wave transformation, we reduce the FSE system to a set of Nonlinear Ordinary Differential Equations (NODEs). We then convert these NODEs into nonlinear algebraic equations using a series solution ansatz. Solving the algebraic system using Maple, we obtain multiple families of soliton solutions for the targeted system. Select solutions are visualized in 3D, 2D, and contour graphical representations, demonstrating the precision and efficacy of our approach. These visualizations reveal intriguing wave profiles, including kink, damped, and periodic patterns, which provide valuable insights into the system’s behavior. This research contributes to the understanding of soliton phenomena in nonlinear fractional systems, paving the way for further explorations in quantum mechanics, optics, and related fields.
Bilal et al. (2026) studied this question.