Existence and controllability results for nonlocal stochastic integro-differential equations

In this work, we deal with the existence, uniqueness and controllability outcomes for stochastic partial integro-differential equations with nonlocal conditions. Our analysis uses Kuratowski's measure of noncompactness, generalized Darbo's fixed point Theorem, Monch fixed point Theorem and Grimmer's resolvent operator theory. Some appropriate conditions for existence, uniqueness and controllability are obtained. Some examples are provided for illustration.

Automated summary

This work focuses on the existence, uniqueness, and controllability outcomes for stochastic partial integro-differential equations with nonlocal conditions. The analysis involves Kuratowski's measure of noncompactness, generalized Darbo's fixed point theorem, Monch's fixed point theorem, and Grimmer's resolvent operator theory. Appropriate conditions for existence, uniqueness, and controllability are established, with examples provided for illustration.