Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation
We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0, where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our anal...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/10368 |
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| _version_ | 1832547544652054528 |
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| author | Moustafa El-Shahed |
| author_facet | Moustafa El-Shahed |
| author_sort | Moustafa El-Shahed |
| collection | DOAJ |
| description | We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:
D0+αu(t)+λa(t) f(u(t))=0, 0<t<1,
u(0)=u′(0)=u′(1)=0,
where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results. |
| format | Article |
| id | doaj-art-0247baa9ed2c4ab69fcc7646d5cbaa0b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0247baa9ed2c4ab69fcc7646d5cbaa0b2025-02-03T06:44:24ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/1036810368Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential EquationMoustafa El-Shahed0Department of Mathematics, College of Education, College of Education, P.O. Box 3771, Unizah-Qasssim, Saudi ArabiaWe are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0, where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.http://dx.doi.org/10.1155/2007/10368 |
| spellingShingle | Moustafa El-Shahed Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation Abstract and Applied Analysis |
| title | Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation |
| title_full | Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation |
| title_fullStr | Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation |
| title_full_unstemmed | Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation |
| title_short | Positive Solutions for Boundary Value Problem of Nonlinear
Fractional Differential Equation |
| title_sort | positive solutions for boundary value problem of nonlinear fractional differential equation |
| url | http://dx.doi.org/10.1155/2007/10368 |
| work_keys_str_mv | AT moustafaelshahed positivesolutionsforboundaryvalueproblemofnonlinearfractionaldifferentialequation |