Extended Riemann-Liouville type fractional derivative operator with applications

P. Agarwal; Juan J. Nieto; M. J. Luo

doi:10.1515/math-2017-0137

Extended Riemann-Liouville type fractional derivative operator with applications

P. Agarwal
, Juan J. Nieto
, M. J. Luo

International College of Engineering
University of Santiago de Compostela
East China Normal University

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

37 Scopus citations

Abstract

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox's H-function are also presented.

Original language	English
Pages (from-to)	1667-1681
Number of pages	15
Journal	Central European Journal of Mathematics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1515/math-2017-0137
State	Published - 29 Dec 2017
Externally published	Yes

Keywords

Extended beta function
Fox H-function
Gamma function
Generating functions
Hypergeometric functions
Integral representations
Mellin transform
Riemann-Liouville fractional derivative

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abstract = "The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox's H-function are also presented.",

keywords = "Extended beta function, Fox H-function, Gamma function, Generating functions, Hypergeometric functions, Integral representations, Mellin transform, Riemann-Liouville fractional derivative",

author = "P. Agarwal and Nieto, \{Juan J.\} and Luo, \{M. J.\}",

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AB - The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox's H-function are also presented.

KW - Extended beta function

KW - Fox H-function

KW - Gamma function

KW - Generating functions

KW - Hypergeometric functions

KW - Integral representations

KW - Mellin transform

KW - Riemann-Liouville fractional derivative

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JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 1

ER -

Extended Riemann-Liouville type fractional derivative operator with applications

Abstract

Keywords

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