Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro-Differential Equations with Infinite Delay

In this paper, we investigate a new class of fractional impulsive stochastic partial integro-differential equations with infinite delay in Hilbert spaces. By using the stochastic analysis theory, fractional calculus, analytic alpha-resolvent operator and the fixed point technique combined with fractional powers of closed operators, we firstly give the existence of of mild solutions and optimal mild solutions for the these equations. Next, the controllability of the controlled fractional impulsive stochastic partial integro-differential systems with not instantaneous impulses is presented. Finally, examples are also given to illustrate our results.