On generalized k-fractional derivative operator

Gauhar Rahman; Shahid Mubeen; Kottakkaran Sooppy Nisar

doi:10.3934/math.2020129

On generalized k-fractional derivative operator

Gauhar Rahman
, Shahid Mubeen
, Kottakkaran Sooppy Nisar

Mathematics

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

28 Scopus citations

Abstract

The principal aim of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to k-hypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and the Wright hypergeometric functions.

Original language	English
Pages (from-to)	1936-1945
Number of pages	10
Journal	AIMS Mathematics
Volume	5
Issue number	3
DOIs	https://doi.org/10.3934/math.2020129
State	Published - 2020

Keywords

Appell’s function
Beta function
Fractional derivative
Hypergeometric function
K-Mittag-Leffler function
K-beta function
K-hypergeometric function
Mellin transform

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10.3934/math.2020129

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title = "On generalized k-fractional derivative operator",

abstract = "The principal aim of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to k-hypergeometric and k-Appell{\textquoteright}s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and the Wright hypergeometric functions.",

keywords = "Appell{\textquoteright}s function, Beta function, Fractional derivative, Hypergeometric function, K-Mittag-Leffler function, K-beta function, K-hypergeometric function, Mellin transform",

author = "Gauhar Rahman and Shahid Mubeen and Nisar, \{Kottakkaran Sooppy\}",

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AU - Rahman, Gauhar

AU - Mubeen, Shahid

AU - Nisar, Kottakkaran Sooppy

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N2 - The principal aim of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to k-hypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and the Wright hypergeometric functions.

AB - The principal aim of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to k-hypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and the Wright hypergeometric functions.

KW - Appell’s function

KW - Beta function

KW - Fractional derivative

KW - Hypergeometric function

KW - K-Mittag-Leffler function

KW - K-beta function

KW - K-hypergeometric function

KW - Mellin transform

UR - https://www.scopus.com/pages/publications/85079899745

U2 - 10.3934/math.2020129

DO - 10.3934/math.2020129

M3 - Article

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VL - 5

SP - 1936

EP - 1945

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 3

ER -

On generalized k-fractional derivative operator

Abstract

Keywords

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