On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

Abstract

We generalize the κ-fractional Hilfer–Katugampola derivative and set some properties of the generalized operator resulting from this. As an application, we demonstrate that the Cauchy problem with this new definition is equivalent to a second kind of Volterra integral equation. We discuss some specific cases for this problem.