Extended Riemann-Liouville type fractional derivative operator with applications

• Autorzy: P. Agarwal , Juan J. Nieto , M.-J. Luo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 33B15: Gamma, beta and polygamma functions
• 33C65: Appell, Horn and Lauricella functions
• 26A33: Fractional derivatives and integrals
• 33C05: Classical hypergeometric functions, 2 F 1
• 33C20: Generalized hypergeometric series, p F q
• 33B20: Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1667-1681

Daty

wydano

2017-01-01

otrzymano

2017-11-16

zaakceptowano

2017-11-30

online

2017-12-29

Twórcy

autor

P. Agarwal

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autor

Juan J. Nieto

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autor

M.-J. Luo

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Identyfikatory

DOI

10.1515/math-2017-0137