Turkish Journal of Mathematics
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