Impulsive Neutral Integrodifferential Systems with Infinite Delay

Impulsive differential equations arise naturally in the description of physical phenomena that are subjected to rapid changes in their states at certain moments of time. The theory of impulsive differential equations has become an active area of investigation due to its applications in fields such as mechanics, electrical engineering, medicine, and so on. Existence and controllability results for impulsive partial neutral functional integrodifferential equation with infinite delay in Banach spaces are discussed. Further, controllability results for impulsive neutral functional integrodifferential equation with infinite delay in Banach spaces are derived. Finally, controllability results for second-order impulsive neutral functional integrodifferential systems with infinite delay in Banach spaces are established. Our approach here is based on the fixed point theorems such as Darbo-Sadovskii's, Monch, Leray-Schauder's of the alternative for multivalued maps, Leray-Schauder's alternative, Banach contraction principle, and Sadovskii's. Examples are provided to illustrated theory.