Mild Solutions of Multipoint Boundary Conditions for Impulsive Fractional Integro-Differential Equations

This study investigates the existence and uniqueness of mild solutions for impulsive fractional integro-differential equations (IFIDEs) in a Banach space, with particular emphasis on the Caputo-Katugampola fractional derivative.The analysis addresses the complexities introduced by impulsive effects and fractional-order dynamics using advanced mathematical tools.Specifically, the contraction mapping principle and Krasnoselskii's fixed point theorem are employed to establish sufficient conditions for the existence and uniqueness of solutions.These methods effectively handle the nonlocal and non smooth nature of IFIDEs.To demonstrate the practical relevance of the theoretical findings, a detailed example is presented, highlighting the applicability of the derived conditions in real-world scenarios.This work contributes to the broader understanding of fractional differential equations in impulsive systems and provides a foundation for further research in this domain.