Some novel existence and uniqueness results for the Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions and their application

In this article, we discuss conditions that are sufficient for the existence of solutions for some ψ-Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions. By applying Krasnoselskii’s and Banach’s fixed point theorems, we investigate the existence and uniqueness of these solutions. Moreover, we have proved its boundedness of the method. We extend some earlier results by introducing and including the ψ-Hilfer fractional derivative, nonlinear integral terms and non-instantaneous impulsive conditions. Finally, we offer an application to explain the consistency of our theoretical results.