Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise

The asymptotically autonomous dynamics in $$H^s(\mathbb R^n)$$ for any $$s\in (0,1)$$ and $$n\in \mathbb {N}$$ are discussed for a class of highly nonlinear nonclassical diffusion equations perturbed by colored noise. The main feature of this model is that the time-dependent drift and diffusion terms have subcritical and superlinear polynomial growth of orders p and q, respectively, satisfying $$\begin{aligned} 2\le 2q