Abstract
In this study, the stochastic fractional Fokas system (SFFS) with M-truncated derivatives is considered. A certain wave transformation is applied to convert this system to a one-dimensional conservative Hamiltonian system. Based on the qualitative theory of dynamical systems, the bifurcation and phase portrait are examined. Utilizing the conserved quantity, we construct some new traveling wave solutions for the SFFS. Due to the fact that the Fokas system is used to explain nonlinear pulse transmission in mono-mode optical fibers, the given solutions may be applied to analyze an extensive variety of crucial physical phenomena. To clarify the effects of the M-truncated derivative and Wiener process, the dynamic behaviors of the various obtained solutions are depicted with 3-D and 2-D curves.
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