<p>In this paper, we consider the time-space fractional stochastic Ginzburg-Landau equations depend on past random effects which has two different fractional time-derivatives and a fractional order space-derivative. The stochastic integral equation equivalent to the time-space fractional stochastic Ginzburg-Landau equation is derived. The local and global existence and uniqueness of the mild solution are obtained. We prove the Sobolev-Hölder regularity and Talagrand’s transportation cost inequality of the mild solution for the time-space fractional stochastic Ginzburg-Landau equation with two different fractional time-derivatives.</p>