Existence of attractors for stochastic diffusion equations with fractional damping and time-varying delay

This paper deals with the well-posedness and existence of attractors of a class of stochastic diffusion equations with fractional damping and time-varying delay on unbounded domains. We first prove the well-posedness and the existence of a continuous non-autonomous cocycle for the equations and the uniform estimates of solutions and the derivative of the solution operators with respect to the time-varying delay. We then show pullback asymptotic compactness of solutions and the existence of random attractors by utilizing the Arzela-Ascoli theorem and the uniform estimates for the derivative of the solution operator in the fractional Sobolev space H alpha (Rn), with 0 < <alpha> < 1.