Extended Caputo k- type fractional derivative operator and its properties

Partial Differential Equations in Applied Mathematics（2024）

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摘要

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.

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关键词

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

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