Existence and Uniqueness of Solutions for Impulsive Evolution Equations With ϕ‐Caputo Fractional Derivatives

Abstract

ABSTRACT This article investigates the existence and uniqueness of solutions to semilinear impulsive evolution equations involving ‐Caputo fractional derivative in Banach spaces. By employing fixed‐point theorems, we derive sufficient conditions for solution existence under nonlocal Cauchy conditions. The proposed model extends several existing frameworks by incorporating both impulsive effects and generalized fractional memory through the ‐function. An illustrative example is provided to demonstrate the applicability of the theoretical results.