Impulsive integro‐differential inclusions with nonlocal conditions: Existence and Ulam's type stability

This article focuses on the existence and Ulam–Hyers–Rassias stability outcomes pertaining to a specific category of impulsive integro‐differential inclusions (with instantaneous and non‐instantaneous impulses). These problems are examined using resolvent operators, drawing from the Grimmer perspective. Our analysis is based on Bohnenblust–Karlin's and Darbo's fixed point theorems for multivalued mappings in Banach spaces. Additionally, we provide an illustrative example to reinforce and demonstrate the validity of our findings.