Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative
This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theore...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/425408 |
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| _version_ | 1832553589335130112 |
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| author | Changyou Wang Haiqiang Zhang Shu Wang |
| author_facet | Changyou Wang Haiqiang Zhang Shu Wang |
| author_sort | Changyou Wang |
| collection | DOAJ |
| description | This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained. |
| format | Article |
| id | doaj-art-18bd5edb88554298956d7f71596d1470 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-18bd5edb88554298956d7f71596d14702025-02-03T05:53:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/425408425408Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo DerivativeChangyou Wang0Haiqiang Zhang1Shu Wang2College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaCollege of Applied Sciences, Beijing University of Technology, Beijing 100124, ChinaThis paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.http://dx.doi.org/10.1155/2012/425408 |
| spellingShingle | Changyou Wang Haiqiang Zhang Shu Wang Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative Discrete Dynamics in Nature and Society |
| title | Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative |
| title_full | Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative |
| title_fullStr | Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative |
| title_full_unstemmed | Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative |
| title_short | Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative |
| title_sort | positive solution of a nonlinear fractional differential equation involving caputo derivative |
| url | http://dx.doi.org/10.1155/2012/425408 |
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