Weak pullback attractors for damped stochastic fractional Schrödinger equation on $$\mathbb{R}$^n

This article discusses the weak pullback attractors for a damped stochastic fractional Schrödinger equation on ${\mathbb{R}}^n$ with $n\ge 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the existence and uniqueness of a global solution for the systems with the nonlinear term $\mathrm{\mid }u{\mathrm{\mid }}^{2\sigma }u$ are proven. Furthermore, we define a mean random dynamical system due to the uniqueness of the solution, which has a unique weak pullback mean random attractor in $L^{\rho }(\mathrm{\Omega };L^2\left({\mathbb{R}}^n\right))$. This result highlights the long-term dynamics of a broad class of stochastic fractional dispersion equations.