Existence results for fractional stochastic semilinear differential equations with nonlocal conditions

Fractional stochastic differential equations arise in the modeling of several phenomena in various fields of science and engineering. Our objective is to contribute to the study of fractional stochastic evolution equations with nonlocal initial conditions. We discuss existence results of mild solutions for stochastic differential equations in Hilbert spaces subject to nonlocal initial conditions. Combining methods from deterministic fractional equations and stochastic analysis theory we provide new set of sufficient conditions and prove the existence of mild solutions for the fractional stochastic differential equations. We rely on fixed point theorems to prove our main results. An example with numerical simulation is provided to illustrate the obtained theory.