A further extension of the extended Riemann-Liouville fractional derivative operator

Martin Bohner; Gauhar Rahman; Shahid Mubeen; Kottakkaran Sooppy Nisar

doi:10.3906/mat-1805-139

A further extension of the extended Riemann-Liouville fractional derivative operator

Martin Bohner
, Gauhar Rahman
, Shahid Mubeen
, Kottakkaran Sooppy Nisar

Mathematics

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

16 Scopus citations

Abstract

The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Original language	English
Pages (from-to)	2631-2642
Number of pages	12
Journal	Turkish Journal of Mathematics
Volume	42
Issue number	5
DOIs	https://doi.org/10.3906/mat-1805-139
State	Published - 2018

Keywords

Appell's function
Extended hypergeometric function
Fractional derivative
Hypergeometric function
Mellin transform

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10.3906/mat-1805-139

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abstract = "The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.",

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AU - Mubeen, Shahid

AU - Nisar, Kottakkaran Sooppy

N1 - Publisher Copyright: © TÜBI˙TAK.

PY - 2018

Y1 - 2018

N2 - The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

AB - The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

KW - Appell's function

KW - Extended hypergeometric function

KW - Fractional derivative

KW - Hypergeometric function

KW - Mellin transform

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IS - 5

ER -

A further extension of the extended Riemann-Liouville fractional derivative operator

Abstract

Keywords

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