Extended Caputo k-type fractional derivative operator and its properties

Abstract

In this paper, we present some extensions of the k-hypergeometric functions and then develop the extended Caputo k-type fractional derivative operator by using two parameters k-Mittag–Leffler function. We also discuss some properties like generating functions and Mellin transform of the new extended Caputo k-type fractional derivative operator.

Keywords

• k-gamma function
• k-beta function
• k-Pochhammer symbol
• k-hypergeometric function
• Mellin transform
• Extended Caputo k-type fractional derivative operator