Existence results for non-instantaneous impulsive Riemann-Liouville fractional stochastic differential equations with delay

Abstract

In this paper, we study a non-instantaneous impulsive fractional stochastic differential equation with delay involving a Riemann-Liouville derivative of order $\alpha\in (1/2, 1)$ with a fixed lower bound. The integral representation of the mild solution is presented, and its existence is proven using Banach's fixed point theorem under sufficient assumptions.