Fractional Sobolev Spaces via Riemann-Liouville Derivatives
Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivit...
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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/10.1155/2013/128043 |
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| Summary: | Using Riemann-Liouville derivatives, we introduce fractional Sobolev
spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we
prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of
some imbeddings. An application to boundary value problems is given as well. |
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| ISSN: | 0972-6802 1758-4965 |