A k-type Caputo fractional derivative operator and its properties

Shilpi Jain; Praveen Agarwal; Parik Laxmi

doi:10.1016/B978-0-44-336484-6.00013-8

A k-type Caputo fractional derivative operator and its properties

Shilpi Jain
, Praveen Agarwal
, Parik Laxmi

Nonlinear Dynamic Research Centre (NDRC)

Poornima College of Engineering
International College of Engineering
Poornima University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter explores the extensions of various k-hypergeometric functions and their integral representations. Additionally, we also introduce a modified version of the Caputo k-fractional derivative operator involving a Confluent k-hypergeometric function as kernel. Additionally, we calculate the extended k-fractional derivatives of some elementary functions. Our main focus is to study how the Caputo k-fractional derivative operator behaves for the exponential function and the k-hypergeometric function. Furthermore, we explore its properties using the Mellin transform.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	63-77
Number of pages	15
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00013-8
State	Published - 1 Jan 2026

Keywords

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

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10.1016/B978-0-44-336484-6.00013-8

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AB - This chapter explores the extensions of various k-hypergeometric functions and their integral representations. Additionally, we also introduce a modified version of the Caputo k-fractional derivative operator involving a Confluent k-hypergeometric function as kernel. Additionally, we calculate the extended k-fractional derivatives of some elementary functions. Our main focus is to study how the Caputo k-fractional derivative operator behaves for the exponential function and the k-hypergeometric function. Furthermore, we explore its properties using the Mellin transform.

KW - Caputo k-fractional derivative operator

KW - Classical beta function

KW - Classical gamma function

KW - Mellin transform

KW - Pochhammer symbol

KW - k-Pochhammer symbol

KW - k-beta function

KW - k-gamma function

KW - k-hypergeometric function

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SP - 63

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BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

A k-type Caputo fractional derivative operator and its properties

Abstract

Keywords

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