Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation
We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)), t∈[0,1], u(0)=0, u′(0)+u′′(0)=0, u′(1)+u′′(1)=0, where α∈(2,3] is a real number, CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuo...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/736108 |
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| author | Jun-Rui Yue Jian-Ping Sun Shuqin Zhang |
| author_facet | Jun-Rui Yue Jian-Ping Sun Shuqin Zhang |
| author_sort | Jun-Rui Yue |
| collection | DOAJ |
| description | We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)), t∈[0,1], u(0)=0, u′(0)+u′′(0)=0, u′(1)+u′′(1)=0, where α∈(2,3] is a real number, CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem. |
| format | Article |
| id | doaj-art-ded9ede641304e8ea04d643358065522 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ded9ede641304e8ea04d6433580655222025-02-03T06:12:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/736108736108Existence of Positive Solution for BVP of Nonlinear Fractional Differential EquationJun-Rui Yue0Jian-Ping Sun1Shuqin Zhang2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Mathematics, China University of Mining and Technology, Beijing 100083, ChinaWe consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)), t∈[0,1], u(0)=0, u′(0)+u′′(0)=0, u′(1)+u′′(1)=0, where α∈(2,3] is a real number, CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.http://dx.doi.org/10.1155/2015/736108 |
| spellingShingle | Jun-Rui Yue Jian-Ping Sun Shuqin Zhang Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation Discrete Dynamics in Nature and Society |
| title | Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation |
| title_full | Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation |
| title_fullStr | Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation |
| title_full_unstemmed | Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation |
| title_short | Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation |
| title_sort | existence of positive solution for bvp of nonlinear fractional differential equation |
| url | http://dx.doi.org/10.1155/2015/736108 |
| work_keys_str_mv | AT junruiyue existenceofpositivesolutionforbvpofnonlinearfractionaldifferentialequation AT jianpingsun existenceofpositivesolutionforbvpofnonlinearfractionaldifferentialequation AT shuqinzhang existenceofpositivesolutionforbvpofnonlinearfractionaldifferentialequation |