This study explores the Formula: see text-dimensional stochastic fractional coupled Fokas system (SFCFS) within optical fibers, addressing the gap in previous research by integrating stochastic noise and fractional dynamics. The novelty of the work lies in the application of the M-truncated fractional derivative (MTFD) and the Improved Modified Sardar Sub-equation Method (IMSSM) to derive new soliton solutions, such as bright, singular and dark singular solitons, providing fresh insights into stochastic-fractional nonlinear wave propagation in optical fibers. In the study, a sensitivity analysis is provided on how fluctuations in system parameters affect the stability and the propagation of solitons. The main results point out that all these factors also strongly influence the behavior of solitons and have potential applications in optical communications, energy forecasting of smart grids and laser pulse propagation. The obtained outcomes are relevant to the optimization of signal integrity within an optical fiber system since they show the role of noise and fractional dynamics. The presentation is carried out in terms of an instructive 2D and 3D graphical representation of the results, aiding the analysis. The study provides a new mathematical framework that contributes to an improved understanding of soliton dynamics and that creates new opportunities in terms of developments related to optical signal processing and energy prediction.
Saleem et al. (Wed,) studied this question.