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

Date

2012

Authors

Srivastava, H.M.
Parmar, Rakesh K.
Chopra, Purnima

Journal Title

Journal ISSN

Volume Title

Publisher

Axioms

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.

Description

Keywords

gamma and beta functions, Eulerian integrals, generating functions, hypergeometric functions, Appell-Lauricella hypergeometric functions, fractional derivative operators, Mellin transforms

Citation

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