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.

DOI

10.3906/mat-2007-67

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, S, & NAEEM, M. N (2021). On the Generalization of $ \kappa $-Fractional Hilfer-Katugampola Derivative with Cauchy Problem. Turkish Journal of Mathematics 45 (1): 110-124. https://doi.org/10.3906/mat-2007-67