Random attractors of fractional p-Laplacian equation driven by colored noise on \({\mathbb {R}}^n\)

This paper is concerned with the asymptotic behavior of the fractional p-Laplacian equation with colored noise on \({\mathbb {R}}^n\) ${\mathbb{R}}^n$ . We first obtain the well-posedness and then prove the existence and uniqueness of tempered pullback random attractors for the fractional p-Laplacian equation with nonlinear diffusion term. Furthermore, we show that the pullback random attractors of the systems driven by linear colored noise converge to that of the corresponding stochastic systems driven by linear white noise under the topology of \(L^2\) $L^2$ as the correlation time of the colored noise approaches zero.