Well-posedness and dynamics of stochastic fractional model for nonlinear optical fiber materials

The current paper is devoted to the well-posedness and dynamics of the stochastic coupled fractional Ginzburg–Landau equation, which describes a class of nonlinear optical fiber materials with active and passive coupled cores. By the commutation estimates and Fourier–Galerkin approximation, the global existence of weak solutions and the uniqueness criterion are established. Moreover, the existence of a global attractor is shown. Finally, we consider the long-time behavior of the stochastic coupled fractional Ginzburg–Landau equation (SCFGL) with multiplicative noise, and prove the existence of a random attractor for the random dynamical system generated by the SCFGL equation.