Effects of Noise and Fractional Derivative on the Exact Solutions of the Stochastic Conformable Fractional Fokas System

This paper mainly investigates the exact solutions and their dynamical behaviors of the stochastic conformable fractional Fokas system (SFFs), offering a more realistic model for optical pulse propagation in monomode optical fibers. By the planar dynamical system method and the extended Kudryashov method, we derive various traveling wave solutions, including bright and dark solitary wave solutions, as well as periodic traveling wave solutions. Furthermore, we explore the impact of multiplicative noise and the order of the conformable derivative on the dynamical behaviors of both soliton solutions and periodic traveling wave solutions. Our findings reveal that the fractional order introduces oscillations in dark solitons and periodic traveling wave solutions, while multiplicative noise causes fluctuations in these solutions. Notably, under the combined influence of multiplicative noise and the conformable derivative, variations in the initial phase result in the fusion and fission of solitons. However, when the fractional order approaches 1, changes in the initial phase solely affect the position and amplitude of the soliton. These results provide a certain theoretical explanation for the phenomenon of optical pulse propagation in fiber optic communication systems, aiding in the understanding of the impact of stochastic factors and fractional order on the behavior of optical pulse propagation.