On stability of nonlocal neutral stochastic integro differential equations with random impulses and Poisson jumps

Abstract

This article aims to examine the existence and Hyers-Ulam stability of non-local random impulsive neutral stochastic integrodifferential delayed equations with Poisson jumps. Initially, we prove the existence of mild solutions to the equations by using the Banach fixed point theorem. Then, we investigate stability via the continuous dependence of solutions on the initial value. Next, we study the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, we give an illustrative example of our main result.

Keywords

• existence of mild solutions
• hyers-ulam (hu) stability
• random impulsive
• stochastic integro differential equations
• time delays