This study aims to investigate the existence of mild solutions for a class of impulsive stochastic integrodifferential equations with state-dependent delay in a real separable Hilbert space, as well as the controllability of these solutions. We offer Sufficient conditions for the existence and controllability results using the fixed point techniques combined with the theory of resolvent operator in Grimmer and analysis stochastic. Finally, we provide an example to illustrate the obtained results.

This paper investigates a functional integral differential equation with state-dependent delay in Banach spaces. This equation's linear part depends on time and generates a linear evolution system. Using the resolvent operator and fixed-point methods theory, we formulate a new set of sufficient conditions for mild solutions of functional integral-differential equations with state-dependent delays. The next part of this study examines the attractiveness of mild solutions for the system under consideration. Finally, we give an example to illustrate the theoretical results.

The goal of this study is to investigate the existence and uniqueness of mild solutions, as well as controllability outcomes, for random integrodifferential equations with state-dependent delay. We prove the existence and uniqueness of mild solutions in the case where the nonlinear term is of the Carath?odory type and meets various weakly compactness conditions. Our research is based on Dardo?s fixed point theorem, M?nch?s fixed point theorem, a random fixed point with a stochastic domain, and Grimmer?s resolvent operator theory. Finally, an example is provided to demonstrate the outcomes that were obtained.