Stochastic impulsive fractional differential evolution equations with infinite delay

TL;DR

This paper studies stochastic impulsive fractional differential equations with infinite delay in Banach spaces, establishing existence, uniqueness, and stability of solutions using approximation and inequalities, with an illustrative example.

Contribution

It introduces new conditions for existence, uniqueness, and stability of solutions to this class of complex stochastic fractional equations with infinite delay.

Findings

Existence and uniqueness of mild solutions are established.

Stability in mean square of solutions is proved.

An example demonstrates the theoretical results.

Abstract

In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly sufficient conditions of the existence and uniqueness of the mild solution for this type of equations are derived by means of the successive approximation. Then we use the Bihari's inequality to get the stability in mean square of the mild solution. Finally an example is presented to illustrate the results.