Existence and Finite-Time Stability Results for Impulsive Caputo-Type Fractional Stochastic Differential Equations with Time Delays

This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelof iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Gronwall-Bellman inequality. As an application, examples are provided to expound our theoretical conclusions.