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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| _version_ | 1832550260263616512 |
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| author | Dariusz Idczak Stanisław Walczak |
| author_facet | Dariusz Idczak Stanisław Walczak |
| author_sort | Dariusz Idczak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1d022df37701488781c068f60fea35e4 |
| 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-1d022df37701488781c068f60fea35e42025-02-03T06:07:07ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/128043128043Fractional Sobolev Spaces via Riemann-Liouville DerivativesDariusz Idczak0Stanisław Walczak1Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, PolandFaculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, PolandUsing 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.http://dx.doi.org/10.1155/2013/128043 |
| spellingShingle | Dariusz Idczak Stanisław Walczak Fractional Sobolev Spaces via Riemann-Liouville Derivatives Journal of Function Spaces and Applications |
| title | Fractional Sobolev Spaces via Riemann-Liouville Derivatives |
| title_full | Fractional Sobolev Spaces via Riemann-Liouville Derivatives |
| title_fullStr | Fractional Sobolev Spaces via Riemann-Liouville Derivatives |
| title_full_unstemmed | Fractional Sobolev Spaces via Riemann-Liouville Derivatives |
| title_short | Fractional Sobolev Spaces via Riemann-Liouville Derivatives |
| title_sort | fractional sobolev spaces via riemann liouville derivatives |
| url | http://dx.doi.org/10.1155/2013/128043 |
| work_keys_str_mv | AT dariuszidczak fractionalsobolevspacesviariemannliouvillederivatives AT stanisławwalczak fractionalsobolevspacesviariemannliouvillederivatives |