Samaira NAZ, Muhammad Nawaz NAEEM

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

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.

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