Stability of random attractors for non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise

The aim of this paper is to establish the stability of pullback random attractors of non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise. In order to overcome the difficulties caused by lack of compact Sobolev embedding on unbounded domains and weak dissipative structure of the equation, we first prove the existence, uniqueness and backward compactness of a special kind of pullback random attractor using the method of spectral decomposition in bounded domains and the uniform tail-estimates of solutions outside bounded domains over the infinite time interval. The measurability of this class of attractors is established by proving that the two classes of defined attractors are equal with respect to two different universes. Finally, the stability of the attractors is investigated by assuming that the time-dependent external forcing term converges to the time-independent external force as the time parameter tends to negative infinity.