An analysis on the boundary control for nonlinear integro-differential evolution systems with impulsive effects and time delays via fixed point theorems

This study investigated the boundary controllability of nonlinear impulsive integro-differential evolution systems (NIIESs) with time-varying delays within Banach spaces. Two classes of NIIESs were considered, and sufficient conditions for their controllability were established using fixed point theorems and semigroup theory. For the first class, Schaefer's fixed point theorem was employed in combination with compact semigroup theory, whereas for the second class, Schauder's fixed point theorem was utilized. The research defined essential hypotheses and mathematical structures to ensure the robustness and applicability of the results. Illustrative examples were provided to confirm the applicability and effectiveness of the developed theoretical framework. This work significantly contributes to the study of partial functional integro-differential equations in nonlinear systems, particularly systems influenced by impulsive effects and time delays, addressing gaps in the existing literature.