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

• Published in: AIMS mathematics Vol. 8; no. 2; pp. 2556 - 2575
• Main Authors: Baleanu, Dumitru, Kasinathan, Ramkumar, Kasinathan, Ravikumar, Sandrasekaran, Varshini
• Format: Journal Article
• Language: English
• Published: AIMS Press 2023
• Subjects: hyers-ulam stability; mean-square exponential stability; random impulse; stochastic differential equations
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2023132

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 M$ \ddot{o} $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.