Abstract
We first prove the existence, uniqueness and continuous dependence of mild solutions to stochastic delay evolution equations with a Caputo fractional derivative:DtαCy(t)=Ay(t)+f(t,yt)+g(t,yt)dW(t)dt,12<α<1. Then, we investigate the asymptotic behavior of mild solutions to fractional stochastic delay evolution equations of the formDtαCy(t)=Ay(t)+It1−αf(t,yt)+[It1−αg(t,yt)]dW(t)dt,0<α<1. In particular, the existence of a global forward attracting set in the mean-square topology is established. A general theorem on the existence of mild solutions is obtained by using α-order fractional resolvent operator theory and the Schauder fixed point theorem.
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