Article Title

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

Authors

SAMAIRA NAZ
MUHAMMAD NAWAZ NAEEM

DOI

10.3906/mat-2007-67

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

First Page

110

Last Page

124

Recommended Citation

NAZ, SAMAIRA and NAEEM, MUHAMMAD NAWAZ (2021) "On the Generalization of $ \kappa $-Fractional Hilfer-Katugampola Derivative with Cauchy Problem," Turkish Journal of Mathematics: Vol. 45: No. 1, Article 7. https://doi.org/10.3906/mat-2007-67
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/7