Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay

This paper studies a class of the fractional stochastic evolution equation with delay. With the aid of the compact semigroup theory and Schauder fixed point theorem, the existence of square-mean S-asymptotically periodic mild solutions is obtained under the situation that the nonlinear functions satisfy certain growth conditions. Moreover, by establishing a new Grönwall integral inequality corresponding to fractional differential equation with delay, the global asymptotic stability of the square-mean S-asymptotically periodic mild solutions are discussed. Finally, an example is given to illustrate our abstract results.