Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order
We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D0+αu(t)+f(t,u(t))=0, 0≤t≤1, 3<α≤4, u(0)=u′(0)=u″(0)=u″(1)=0, where D0+α denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/165641 |
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| author | J. Caballero J. Harjani K. Sadarangani |
| author_facet | J. Caballero J. Harjani K. Sadarangani |
| author_sort | J. Caballero |
| collection | DOAJ |
| description | We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D0+αu(t)+f(t,u(t))=0, 0≤t≤1, 3<α≤4, u(0)=u′(0)=u″(0)=u″(1)=0, where D0+α denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results. |
| format | Article |
| id | doaj-art-28c0e0b3c4d74790aa50e60c4bb626f6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-28c0e0b3c4d74790aa50e60c4bb626f62025-02-03T06:08:26ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/165641165641Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional OrderJ. Caballero0J. Harjani1K. Sadarangani2Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, SpainDepartamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, SpainDepartamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, SpainWe are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D0+αu(t)+f(t,u(t))=0, 0≤t≤1, 3<α≤4, u(0)=u′(0)=u″(0)=u″(1)=0, where D0+α denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.http://dx.doi.org/10.1155/2011/165641 |
| spellingShingle | J. Caballero J. Harjani K. Sadarangani Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order Abstract and Applied Analysis |
| title | Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order |
| title_full | Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order |
| title_fullStr | Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order |
| title_full_unstemmed | Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order |
| title_short | Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order |
| title_sort | existence and uniqueness of positive solution for a boundary value problem of fractional order |
| url | http://dx.doi.org/10.1155/2011/165641 |
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