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

Axioms

H. M. Srivastava²  Rakesh K. Parmar¹ 

[1] Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan, India;;Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

关键词: gamma and beta functions;    Eulerian integrals;    generating functions;    hypergeometric functions;    Appell-Lauricella hypergeometric functions;    fractional derivative operators;    Mellin transforms;   

DOI  :  10.3390/axioms1030238

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.