Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations
We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where 0<β<α<1, D0+α is the standard Riemann-Liouville differentiation and f:[0,1]×[0,∞)→[0,∞) is con...
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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/10.1155/2012/837437 |
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| author | D. Baleanu H. Mohammadi Sh. Rezapour |
| author_facet | D. Baleanu H. Mohammadi Sh. Rezapour |
| author_sort | D. Baleanu |
| collection | DOAJ |
| description | We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where 0<β<α<1, D0+α is the standard Riemann-Liouville differentiation and f:[0,1]×[0,∞)→[0,∞) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained. |
| format | Article |
| id | doaj-art-a76bc8364e024b62b9f951986a930d1d |
| 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-a76bc8364e024b62b9f951986a930d1d2025-02-03T05:54:41ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/837437837437Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential EquationsD. Baleanu0H. Mohammadi1Sh. Rezapour2Department of Mathematics, Cankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, TurkeyDepartment of Mathematics, Azarbaijan University of Shahid Madani, Tabriz, IranDepartment of Mathematics, Azarbaijan University of Shahid Madani, Tabriz, IranWe investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem D0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where 0<β<α<1, D0+α is the standard Riemann-Liouville differentiation and f:[0,1]×[0,∞)→[0,∞) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.http://dx.doi.org/10.1155/2012/837437 |
| spellingShingle | D. Baleanu H. Mohammadi Sh. Rezapour Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations Abstract and Applied Analysis |
| title | Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations |
| title_full | Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations |
| title_fullStr | Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations |
| title_full_unstemmed | Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations |
| title_short | Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations |
| title_sort | positive solutions of an initial value problem for nonlinear fractional differential equations |
| url | http://dx.doi.org/10.1155/2012/837437 |
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