Exploring Abundant Solutions for the M-fractional Chiral Nonlinear Schrodinger Equation with Time-Dependent Coefficients by Using the Sardar Subequation Method

In this study, we look at the M-fractional Chiral nonlinear Schrödinger equation (MFCNSE) with time-dependent coefficients, which is a useful model for modeling asymmetric and memory-dependent wave propagation in complex nonlinear media. The Sardar subequation method is utilized to produce a variety of exact fractional solutions, including hyperbolic and trigonometric wave forms. These exact solutions offer detailed insights into very complex nonlinear processes such as wave localization, modulation instability, and energy transfer in nonuniform environments. The discovered solutions are relevant because they have direct applications in crucial domains such as plasma physics, nonlinear optics, and quantum mechanical models with nontrivial symmetry. Furthermore, a detailed study is provided to show how changes in the M-truncated derivative order and time-dependent coefficients have a major impact on the qualitative structure and dynamical behavior of wave solutions.