Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions

The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples...

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Detalles Bibliográficos
Autores principales: Zhou, Xian-Feng, Liu, Song, Zhang, Zhixin, Jiang, Wei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3835843/
https://www.ncbi.nlm.nih.gov/pubmed/24302864
http://dx.doi.org/10.1155/2013/605412
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author Zhou, Xian-Feng
Liu, Song
Zhang, Zhixin
Jiang, Wei
author_facet Zhou, Xian-Feng
Liu, Song
Zhang, Zhixin
Jiang, Wei
author_sort Zhou, Xian-Feng
collection PubMed
description The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.
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spelling pubmed-38358432013-12-03 Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions Zhou, Xian-Feng Liu, Song Zhang, Zhixin Jiang, Wei ScientificWorldJournal Research Article The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results. Hindawi Publishing Corporation 2013-10-31 /pmc/articles/PMC3835843/ /pubmed/24302864 http://dx.doi.org/10.1155/2013/605412 Text en Copyright © 2013 Xian-Feng Zhou et al. 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
Zhou, Xian-Feng
Liu, Song
Zhang, Zhixin
Jiang, Wei
Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title_full Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title_fullStr Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title_full_unstemmed Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title_short Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
title_sort monotonicity, concavity, and convexity of fractional derivative of functions
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3835843/
https://www.ncbi.nlm.nih.gov/pubmed/24302864
http://dx.doi.org/10.1155/2013/605412
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AT liusong monotonicityconcavityandconvexityoffractionalderivativeoffunctions
AT zhangzhixin monotonicityconcavityandconvexityoffractionalderivativeoffunctions
AT jiangwei monotonicityconcavityandconvexityoffractionalderivativeoffunctions

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