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Axioms 2012, 1(3), 238-258; doi:10.3390/axioms1030238
Article

A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions

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Received: 29 June 2012 / Revised: 8 September 2012 / Accepted: 12 September 2012 / Published: 5 October 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
View Full-Text   |   Download PDF [238 KB, 8 October 2012; original version 5 October 2012]

Abstract

Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1]. The main object of this paper is to present a further generalization of the extended fractional derivative operator and apply the generalized extended fractional derivative operator to derive linear and bilinear generating relations for the generalized extended Gauss, Appell and Lauricella hypergeometric functions in one, two and more variables. Some other properties and relationships involving the Mellin transforms and the generalized extended fractional derivative operator are also given.
Keywords: gamma and beta functions; Eulerian integrals; generating functions; hypergeometric functions; Appell–Lauricella hypergeometric functions; fractional derivative operators; Mellin transforms gamma and beta functions; Eulerian integrals; generating functions; hypergeometric functions; Appell–Lauricella hypergeometric functions; fractional derivative operators; Mellin transforms
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Srivastava, H.M.; Parmar, R.K.; Chopra, P. A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions. Axioms 2012, 1, 238-258.

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