Existence, stability and controllability results of stochastic differential equations with non-instantaneous impulses

Abstract

This paper is devoted to the study of a new class of non-instantaneous impulsive stochastic differential equations driven by mixed fractional Brownian motion in separable Hilbert spaces. Based on the stochastic analysis theory, analytic semigroup theory of linear operators, fractional powers of operators, and a fixed point technique, a new set of sufficient conditions are derived to ensure the existence and uniqueness of mild solutions for the proposed stochastic system. Moreover, we also investigate the asymptotic behaviour of mild solutions and controllability results for the proposed stochastic system. Finally, an example is given to demonstrate the applicability of our main results.