Next Article in Journal
The Sum of a Finite Group of Weights of a Hopf Algebra
Previous Article in Journal
Hopf Algebra Symmetries of an Integrable Hamiltonian for Anyonic Pairing
Previous Article in Special Issue
Fat Triangulations, Curvature and Quasiconformal Mappings
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

1
, 2
 and 3
Received: 29 June 2012; in revised form: 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, updated 8 October 2012; original version uploaded 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


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.

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.

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.


Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert