Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian
We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut, 1<t<e, u1=u′1=u′e=0, Dαu1=Dαue=0, where the continuous function f:1,e×0,+∞→[0,+∞), 2<α≤3, 1<β≤2. Dα denotes the standard Hadamard fractional derivative of the order α, the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/951643 |
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| _version_ | 1832567007809110016 |
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| author | Ya-ling Li Shi-you Lin |
| author_facet | Ya-ling Li Shi-you Lin |
| author_sort | Ya-ling Li |
| collection | DOAJ |
| description | We study the following nonlinear fractional differential equation involving the p-Laplacian operator
DβφpDαut=ft,ut, 1<t<e, u1=u′1=u′e=0, Dαu1=Dαue=0, where the continuous function f:1,e×0,+∞→[0,+∞), 2<α≤3, 1<β≤2. Dα denotes the standard Hadamard fractional derivative of the order α, the constant p>1, and the p-Laplacian operator φps=sp-2s. We show some results about the existence and the uniqueness of the positive solution by using fixed point theorems and the properties of Green's function and the p-Laplacian operator. |
| format | Article |
| id | doaj-art-55879d46c8344c9f849a4aa593b74168 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-55879d46c8344c9f849a4aa593b741682025-02-03T01:02:35ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/951643951643Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-LaplacianYa-ling Li0Shi-you Lin1School of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan 571158, ChinaSchool of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan 571158, ChinaWe study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut, 1<t<e, u1=u′1=u′e=0, Dαu1=Dαue=0, where the continuous function f:1,e×0,+∞→[0,+∞), 2<α≤3, 1<β≤2. Dα denotes the standard Hadamard fractional derivative of the order α, the constant p>1, and the p-Laplacian operator φps=sp-2s. We show some results about the existence and the uniqueness of the positive solution by using fixed point theorems and the properties of Green's function and the p-Laplacian operator.http://dx.doi.org/10.1155/2013/951643 |
| spellingShingle | Ya-ling Li Shi-you Lin Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian Journal of Function Spaces and Applications |
| title | Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian |
| title_full | Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian |
| title_fullStr | Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian |
| title_full_unstemmed | Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian |
| title_short | Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian |
| title_sort | positive solution for the nonlinear hadamard type fractional differential equation with p laplacian |
| url | http://dx.doi.org/10.1155/2013/951643 |
| work_keys_str_mv | AT yalingli positivesolutionforthenonlinearhadamardtypefractionaldifferentialequationwithplaplacian AT shiyoulin positivesolutionforthenonlinearhadamardtypefractionaldifferentialequationwithplaplacian |