Novel results on impulsive Caputo–Hadamard fractional Volterra–Fredholm integro-differential equations with a new modeling integral boundary value problem

The purpose of this paper is to investigate, the existence and uniqueness of solutions for nonlinear fractional impulsive fractional Volterra–Fredholm integro-differential equations of the Caputo–Hadamard type, with a new modeling integral boundary value problem. The Krasnoselskii fixed-point theorem, Schaefer’s fixed point theorem, and the Banach contraction principle serve as the basis of this unique strategy and are used to achieve the desired results. An example illustrates the theoretical findings.