Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation

In this study, the fractional-stochastic Fokas-Lenells equation is considered in the Stratonovich framework. The new extended direct algebraic method is applied to construct various types of fractional solutions, including trigonometric, complex, hyperbolic, and exponential forms. Given the equation’s broad applications in telecommunication systems, complex system theory, quantum field theory, and quantum mechanics, the derived solutions have potential to model a variety of significant physical phenomena. To further illustrate the influence of multiplicative noise and fractional derivatives, multiple 3D plots are presented, highlighting their impact on the analytical behavior of the system. Secondly , by applying a Galilean transformation, the model is reformulated into a planar dynamical system, allowing for in-depth qualitative analysis. The sensitivity analysis of the model is performed, along with an examination of quasi-periodic patterns emerging from perturbations. The simulation results reveal that adjusting the amplitude and frequency parameters significantly alters the dynamic behavior of the system. The quasi-periodic behavior is further analyzed through time analysis, multi-stability, and Lyapunov exponents. Our results highlight the impact of the method on system dynamics and demonstrate its effectiveness in studying solitons and phase behavior in nonlinear models. These findings offer new insights into how the proposed approach can induce significant changes in system dynamics, emphasizing its utility in the analysis of soliton solutions and phase visualizations in various nonlinear models. By generating state-dependent oscillations, multiplicative noise has a substantial impact on the dynamics of the system. These fluctuations can either improve or decrease stability and result in complicated behaviors. The completion of stochastic systems affected by internal or external noise sources requires an understanding of this interaction.