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 and Statistics

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

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	American English
Journal	Turkish Journal of Mathematics
Volume	42
DOIs	https://doi.org/10.3906/mat-1805-139
State	Published - Sep 1 2018

Keywords

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

Disciplines

Mathematics
Statistics and Probability

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10.3906/mat-1805-139License: Unspecified

A Further Extension of the Extended Riemann-Liouville FractionalFinal published version, 258 KBLicense: Unspecified

Cite this

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title = "A Further Extension of the Extended Riemann-Liouville Fractional Derivative Operator",

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.",

keywords = "Appell's function, Extended hypergeometric function, Fractional derivative, Hypergeometric function, Mellin transform",

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

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AU - Mubeen, Shahid

AU - Nisar, Kottakkaran Sooppy

PY - 2018/9/1

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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

UR - https://scholarsmine.mst.edu/math_stat_facwork/756

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DO - 10.3906/mat-1805-139

M3 - Article

VL - 42

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

ER -

A Further Extension of the Extended Riemann-Liouville Fractional Derivative Operator

Abstract

Keywords

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