Fractional Calculus of the Generalized Mittag-Leffler Type Function

We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (...

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Detalles Bibliográficos
Autores principales: Kumar, Dinesh, Kumar, Sunil
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897335/
https://www.ncbi.nlm.nih.gov/pubmed/27437505
http://dx.doi.org/10.1155/2014/907432
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author Kumar, Dinesh
Kumar, Sunil
author_facet Kumar, Dinesh
Kumar, Sunil
author_sort Kumar, Dinesh
collection PubMed
description We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.
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spelling pubmed-48973352016-07-19 Fractional Calculus of the Generalized Mittag-Leffler Type Function Kumar, Dinesh Kumar, Sunil Int Sch Res Notices Research Article We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper. Hindawi Publishing Corporation 2014-08-18 /pmc/articles/PMC4897335/ /pubmed/27437505 http://dx.doi.org/10.1155/2014/907432 Text en Copyright © 2014 D. Kumar and S. Kumar. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Kumar, Dinesh
Kumar, Sunil
Fractional Calculus of the Generalized Mittag-Leffler Type Function
title Fractional Calculus of the Generalized Mittag-Leffler Type Function
title_full Fractional Calculus of the Generalized Mittag-Leffler Type Function
title_fullStr Fractional Calculus of the Generalized Mittag-Leffler Type Function
title_full_unstemmed Fractional Calculus of the Generalized Mittag-Leffler Type Function
title_short Fractional Calculus of the Generalized Mittag-Leffler Type Function
title_sort fractional calculus of the generalized mittag-leffler type function
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897335/
https://www.ncbi.nlm.nih.gov/pubmed/27437505
http://dx.doi.org/10.1155/2014/907432
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AT kumarsunil fractionalcalculusofthegeneralizedmittaglefflertypefunction

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