On the initial value problem of fractional stochastic evolution equations in Hilbert spaces

In this article, we are concerned with the initialvalue problem of fractional stochastic evolution equations in real separable Hilbert spaces. The existence of saturatedmild solutions and global mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growthconditions by using α-order fractional resolvent operator theory, the Schauder fixed point theorem and piecewise extension method. Furthermore, the continuous dependence of mild solutions on initial values and orders as well as the asymptotical stability in p-th moment of mild solutions for the studied problem have also been discussed. The results obtained in thispaper improve and extend some related conclusions on this topic. Anexample is also given to illustrate the feasibility of our abstract results.