Controllability of Hammerstein impulsive integro-differential equation driven by Atangana Baleanu Caputo fractional derivative

We investigate the existence, uniqueness, and controllability of a class of fractional differential system, specifically system containing semi-linear neutral integro-delay equations with impulsive effects, governed by the Atangana-Baleanu Caputo fractional derivatives. Using the Banach fixed-point theorem, we establish sufficient conditions for the well-posedness of the system. Furthermore, by combining semi-group theory with Darbo’s fixed-point theorem, the controllability results are obtained. The chosen fractional derivative effectively captures memory and hereditary properties, providing a refined representation of the system’s complex dynamics. To address analytical challenges arising from impulsive effects and time delays, we employ the Kuratowski measure of non-compactness. A numerical example, given at the end, illustrates the practical applicability of the theoretical findings. Overall, this work offers a robust and comprehensive analytical framework for modeling and controlling intricate fractional-order dynamics, by supplying valuable tools for addressing problems in engineering, physics, and related applied sciences.