Certain Extended Type Hypergeometric Functions of Two and Three Variables

Shaher Momani; Praveen Agarwal; Shilpi Jain; Clemente Cesarano

doi:10.5269/bspm.63437

Certain Extended Type Hypergeometric Functions of Two and Three Variables

Shaher Momani
, Praveen Agarwal
, Shilpi Jain
, Clemente Cesarano

Nonlinear Dynamic Research Centre (NDRC)

University of Jordan
International College of Engineering
Poornima College of Engineering
International Telematic University Uninettuno

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

Abstract

The major objective of the present article is to study the new extension of hypergeometric functions of two and three variables by using the 2 parameters Mittag-Leffler function. In the present article, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville type fractional derivative operator.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	43
DOIs	https://doi.org/10.5269/bspm.63437
State	Published - 16 Jan 2025

Keywords

26A33
26D10
33B15
33C05
33C20
33C65
Appell’s hypergeometric functions of two variables
Beta function
Hypergeometric function
Lauricella’s hypergeometric function of three variables
Mittag-Leffler function
Riemann-Liouville fractional derivative operator

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10.5269/bspm.63437

Cite this

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abstract = "The major objective of the present article is to study the new extension of hypergeometric functions of two and three variables by using the 2 parameters Mittag-Leffler function. In the present article, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville type fractional derivative operator.",

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AU - Momani, Shaher

AU - Agarwal, Praveen

AU - Jain, Shilpi

AU - Cesarano, Clemente

N1 - Publisher Copyright: © Soc. Paran. de Mat.

PY - 2025/1/16

Y1 - 2025/1/16

N2 - The major objective of the present article is to study the new extension of hypergeometric functions of two and three variables by using the 2 parameters Mittag-Leffler function. In the present article, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville type fractional derivative operator.

AB - The major objective of the present article is to study the new extension of hypergeometric functions of two and three variables by using the 2 parameters Mittag-Leffler function. In the present article, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville type fractional derivative operator.

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KW - 26D10

KW - 33B15

KW - 33C05

KW - 33C20

KW - 33C65

KW - Appell’s hypergeometric functions of two variables

KW - Beta function

KW - Hypergeometric function

KW - Lauricella’s hypergeometric function of three variables

KW - Mittag-Leffler function

KW - Riemann-Liouville fractional derivative operator

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DO - 10.5269/bspm.63437

M3 - Article

AN - SCOPUS:105026216348

SN - 0037-8712

VL - 43

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JO - Boletim da Sociedade Paranaense de Matematica

JF - Boletim da Sociedade Paranaense de Matematica

ER -

Certain Extended Type Hypergeometric Functions of Two and Three Variables

Abstract

Keywords

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