Nonlocal Problem for Fractional Stochastic Evolution Equations with Solution Operators

Abstract

Abstract In this article, we are concerned with a class of fractional stochastic evolution equations with nonlocal initial conditions in Hilbert spaces. The existence of mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using fractional calculations, Schauder fixed point theorem, stochastic analysis theory, α-order fractional solution operator theory and α-resolvent family theory. The results obtained in this paper improve and extend some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract result.