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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. View Full-Text
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
MDPI and ACS Style

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. https://doi.org/10.3390/axioms1030238

AMA Style

Srivastava HM, Parmar RK, Chopra P. A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions. Axioms. 2012; 1(3):238-258. https://doi.org/10.3390/axioms1030238

Chicago/Turabian Style

Srivastava, H. M.; Parmar, Rakesh K.; Chopra, Purnima. 2012. "A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions" Axioms 1, no. 3: 238-258. https://doi.org/10.3390/axioms1030238

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