Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation
We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0, 0<t<1, 2<α≤3, u(0)=u'(0)=0, u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riem...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/826580 |
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| author | I. J. Cabrera J. Harjani K. B. Sadarangani |
| author_facet | I. J. Cabrera J. Harjani K. B. Sadarangani |
| author_sort | I. J. Cabrera |
| collection | DOAJ |
| description | We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0, 0<t<1, 2<α≤3, u(0)=u'(0)=0, u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riemann-Liouville fractional derivative, f:[0,1]×[0,∞)→[0,∞) is a continuous function, ai≥0 for i=1,2,…,m-2, and 0<ξ1<ξ2<⋯<ξm-2<1. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results. |
| format | Article |
| id | doaj-art-13e2847f38ad4f468a9d15d28a17afb2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-13e2847f38ad4f468a9d15d28a17afb22025-02-03T06:08:19ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/826580826580Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential EquationI. J. Cabrera0J. Harjani1K. B. 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 a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0, 0<t<1, 2<α≤3, u(0)=u'(0)=0, u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riemann-Liouville fractional derivative, f:[0,1]×[0,∞)→[0,∞) is a continuous function, ai≥0 for i=1,2,…,m-2, and 0<ξ1<ξ2<⋯<ξm-2<1. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.http://dx.doi.org/10.1155/2012/826580 |
| spellingShingle | I. J. Cabrera J. Harjani K. B. Sadarangani Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation Abstract and Applied Analysis |
| title | Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_full | Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_fullStr | Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_full_unstemmed | Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_short | Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_sort | positive and nondecreasing solutions to an m point boundary value problem for nonlinear fractional differential equation |
| url | http://dx.doi.org/10.1155/2012/826580 |
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