# Weighted hypergeometric functions and fractional derivative

Ontology type: schema:ScholarlyArticle      Open Access: True

### Article Info

DATE

2017-04-05

AUTHORS ABSTRACT

We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator. Then some of the considered hypergeometric functions are determined in terms of the generalized Mittag-Leffler function E(ρj),λ(γj),(lj)[z1,…,zr]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{(\rho_{j}),\lambda}^{(\gamma_{j}),(l_{j})}[z_{1},\ldots,z_{r}]$\end{document} (Mainardi in Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, 2010) and the generalized polynomials Snm[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_{n}^{m}[x]$\end{document} (Srivastava in Indian J. Math. 14:1-6, 1972). The boundary behavior of some other class of weighted hypergeometric functions is described in terms of Frostman’s α-capacity. Finally, an application is given using our fractional operator in the problem of fractional calculus of variations. More... »

PAGES

105

### References to SciGraph publications

• 2001-09. A Note on the Hypergeometric Mean Value in COMPUTATIONAL METHODS AND FUNCTION THEORY
• 2010-03-31. Lipschitz spaces and QK type spaces in SCIENCE CHINA MATHEMATICS
• 2014-09-13. A Note on Generating Functions Involving the Generalized Gauss Hypergeometric Functions in NATIONAL ACADEMY SCIENCE LETTERS
• 2014-06-25. A Tutorial Review on Fractal Spacetime and Fractional Calculus in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
• ### Journal

TITLE

Advances in Continuous and Discrete Models

ISSUE

1

VOLUME

2017

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-017-1165-7

DOI

http://dx.doi.org/10.1186/s13662-017-1165-7

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