Exploring Soliton Solutions of the Nonlinear Time-Fractional Schrödinger Model via M-Truncated and Atangana-Baleanu Fractional Operators

This study investigates the nonlinear time-fractional Schrödinger model by utilizing this prototype in fields like nonlinear optics, plasma physics, soliton theory, quantum field theory, and dark matter/neural network modeling. It analyzes the equation to reveal key insights into fundamental physical phenomena, advancing novel technological applications. The paper presents fractional derivatives using M-truncated and Atangana-Baleanu operators. The approach employs Bäcklund transformation and Wang’s direct mapping method to derive soliton solutions, including exponential, sin-cos, sinh-cosh, rational, trigonometric, and hyperbolic forms. The present study constructs the energy balance method via the problem’s Hamiltonian and variational principle, offering a promising approach. It complements analytical results with numerical simulations to enhance understanding of solution behavior. The study provides foundations for further exploration, ensuring practical, reliable solutions for complex nonlinear problems. The methods prove robust, efficient, and applicable to diverse nonlinear PDEs.