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Volume :37 Issue : 1 2010      Add To Cart                                                                    Download

Caputo-type fractional derivative of a hypergeometric integral operator

Auther : ALKA RAO*, MRIDULA GARG**AND S.L. KALLA***

*Department of Mathematics, M.P. Govt. P.G. College, Chittorgarh, 312001, India.

E-mail:alkarao.ar@rediffmail.com

**Department of Mathematics, University of Rajasthan, Jaipur, 302055, India.

E-mail: gargmridula@gmail.com

***‡Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait.[Institute of Mathematics, VIHE, 15 B, Pal-Link Road, Jodhpur-342008 India]

E-mail: shyamkalla@gmail.com

 

ABSTRACT

 

In the present paper, we investigate Caputo-type derivatives of a hypergeometric fractional integral operator. The relation between this definition and the classical definition of a fractional derivative is that the operations of fractional integration and differentiation are interchanged. Our operator generalizes the Caputo fractional derivative and also the Caputo-type modification of the Erdإlyi-Kober operator defined by Gorenflo, Luchko and Mainardi, in the light of recent work by Luchko and Gorenflo.

 

Keywords: Fractional integrals and derivatives; Gauss hypergeometric function; Caputo fractional derivative; Hypergeometric fractional integral operators.

MSC 2000: 26A33, 33C05, 45J05

 

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