Time–space fractional stochastic Ginzburg–Landau equation driven by fractional Brownian motion.

The current paper is devoted to the time–space fractional Ginzburg–Landau equation driven by fractional Brownian motion. The spatial–temporal regularity of the nonlocal stochastic convolution is firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag-Leffler functions. Finally, the numerical simulations for the time-fractional stochastic Ginzburg–Landau equation are provided to verify the mathematical analysis results. [ABSTRACT FROM AUTHOR]