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 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada 2 Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan, India 3 Department of Mathematics, Marudhar Engineering College, Raisar, NH-11 Jaipur Road, Bikaner 334001, Rajasthan, India
* Author to whom correspondence should be addressed.
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)
PDF Full-text Download PDF Full-Text [238 KB, Updated Version, uploaded 8 October 2012 16:11 CEST]
The original version is still available [238 KB, uploaded 5 October 2012 14:01 CEST]
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

Article Statistics

Load and display the download statistics.

Citations to this Article

Cite This Article

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