Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem
By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some resu...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/540351 |
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| _version_ | 1832558853454036992 |
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| author | Wenzhe Xie Jing Xiao Zhiguo Luo |
| author_facet | Wenzhe Xie Jing Xiao Zhiguo Luo |
| author_sort | Wenzhe Xie |
| collection | DOAJ |
| description | By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al-Refai (2012). As applications, an example is presented to illustrate our main results. |
| format | Article |
| id | doaj-art-41efd8dbb0444cecb0c25a638b4a1515 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-41efd8dbb0444cecb0c25a638b4a15152025-02-03T01:31:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/540351540351Existence of Solutions for Riemann-Liouville Fractional Boundary Value ProblemWenzhe Xie0Jing Xiao1Zhiguo Luo2Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaDepartment of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, ChinaDepartment of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaBy using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al-Refai (2012). As applications, an example is presented to illustrate our main results.http://dx.doi.org/10.1155/2014/540351 |
| spellingShingle | Wenzhe Xie Jing Xiao Zhiguo Luo Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem Abstract and Applied Analysis |
| title | Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem |
| title_full | Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem |
| title_fullStr | Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem |
| title_full_unstemmed | Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem |
| title_short | Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem |
| title_sort | existence of solutions for riemann liouville fractional boundary value problem |
| url | http://dx.doi.org/10.1155/2014/540351 |
| work_keys_str_mv | AT wenzhexie existenceofsolutionsforriemannliouvillefractionalboundaryvalueproblem AT jingxiao existenceofsolutionsforriemannliouvillefractionalboundaryvalueproblem AT zhiguoluo existenceofsolutionsforriemannliouvillefractionalboundaryvalueproblem |