Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces

This paper is concerned with the existence of -mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space. We assume that the linear part generates a compact, analytic and uniformly bounded semigroup, the nonlinear part satisfies some local growth conditions in Hilbert space and the nonlocal term satisfies some local growth conditions in fractional power space . The result obtained in this paper improves and extends some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract result.