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.
$\kappa$-gamma function, $\kappa$-Mittag-Leffler function, $\kappa$-Riemann-Liouville fractional integral, generalized $\kappa$-fractional derivative
NAZ, SAMAIRA and NAEEM, MUHAMMAD NAWAZ
"On the Generalization of $ \kappa $-Fractional Hilfer-Katugampola Derivative with Cauchy Problem,"
Turkish Journal of Mathematics: Vol. 45:
1, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/7