Extended Caputo k-type fractional derivative operator and its properties

Parik Laxmi; Shilpi Jain; Praveen Agarwal

doi:10.1016/j.padiff.2024.100625

Extended Caputo k-type fractional derivative operator and its properties

Parik Laxmi
, Shilpi Jain
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Poornima University
International College of Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Article number	100625
Journal	Partial Differential Equations in Applied Mathematics
Volume	9
DOIs	https://doi.org/10.1016/j.padiff.2024.100625
State	Published - Mar 2024

Keywords

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

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10.1016/j.padiff.2024.100625

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

author = "Parik Laxmi and Shilpi Jain and Praveen Agarwal",

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AU - Jain, Shilpi

AU - Agarwal, Praveen

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N2 - 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.

AB - 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.

KW - Extended Caputo k-type fractional derivative operator

KW - Mellin transform

KW - k-Pochhammer symbol

KW - k-beta function

KW - k-gamma function

KW - k-hypergeometric function

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JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

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Extended Caputo k-type fractional derivative operator and its properties

Abstract

Keywords

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