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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |