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, 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
