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

Abstract

In this paper, we investigate a fractional stochastic differential equation with delay and noninstantaneous impulses involving the Riemann-Liouville derivative of order ? ? (1/2, 1) with a fixed lower bound. The integral representation of the mild solution is presented, and existence results are established using Banach?s fixed point theorem under appropriate assumptions. An example is provided to illustrate the main result.