Optimality of fractional impulsive partial stochastic differential systems with analytic sectorial operators and controls

Abstract

In this paper, we study a class of fractional impulsive partial stochastic differential systems with analytic sectorial operators and not instantaneous impulses in separable Hilbert spaces. Firstly, the existence of mild solutions and optimal mild solutions investigated by utilizing the theory of analytic sectorial operators, stochastic analysis, suitable fixed point theorems with the Hausdorff measure of noncompactness. Secondly, the question of exact controllability of these control systems is considered too. Finally, an example to illustrate the applications of main results is also given.