On the Generalization of $ \kappa $-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

Authors: SAMAIRA NAZ, MUHAMMAD NAWAZ NAEEM

Abstract: We generalize the $\kappa$-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.

Keywords: $\kappa$-gamma function, $\kappa$-Mittag-Leffler function, $\kappa$-Riemann-Liouville fractional integral, generalized $\kappa$-fractional derivative

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