Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions

In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and Mo spacing diaeresis nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.

Automated summary

This article focuses on the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations with noncompact semigroups and resolvent operators in Hilbert spaces. The authors use Hausdorff measures of noncompactness and the Mo spacing diaeresis nch fixed point theorem to prove the existence of mild solutions. They also investigate stability results, including continuous dependence of initial conditions, Hyers-Ulam stability, and mean-square stability of the system, by developing new analysis techniques and establishing an improved inequality.