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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/605412 |
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| _version_ | 1832554880014745600 |
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| author | Xian-Feng Zhou Song Liu Zhixin Zhang Wei Jiang |
| author_facet | Xian-Feng Zhou Song Liu Zhixin Zhang Wei Jiang |
| author_sort | Xian-Feng Zhou |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-82186938b0ac4661851185ee92377948 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-82186938b0ac4661851185ee923779482025-02-03T05:50:16ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/605412605412Monotonicity, Concavity, and Convexity of Fractional Derivative of FunctionsXian-Feng Zhou0Song Liu1Zhixin Zhang2Wei Jiang3School of Mathematical Sciences, Anhui University, Hefei 230039, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230039, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230039, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230039, ChinaThe 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.http://dx.doi.org/10.1155/2013/605412 |
| spellingShingle | Xian-Feng Zhou Song Liu Zhixin Zhang Wei Jiang Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions The Scientific World Journal |
| 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 |
| url | http://dx.doi.org/10.1155/2013/605412 |
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