(ω,c)-Periodic Solution to Semilinear Integro-Differential Equations with Hadamard Derivatives

This study aims to prove the existence and uniqueness of the (ω,c)-periodic solution as a specific solution to Hadamard impulsive boundary value integro-differential equations with fixed lower limits. The results are proven using the Banach contraction, Schaefer’s fixed point theorem, and the Arzelà–Ascoli theorem. Furthermore, we establish the necessary conditions for a set of solutions to the explored boundary values with impulsive fractional differentials. Finally, we present two examples as applications for our results.