Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales
By the concept of fractional derivative of Riemann-Liouville on time scales, we first introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Then, we prove equivalence of some norms in th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/7149356 |
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| _version_ | 1832551603628933120 |
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| author | Xing Hu Yongkun Li |
| author_facet | Xing Hu Yongkun Li |
| author_sort | Xing Hu |
| collection | DOAJ |
| description | By the concept of fractional derivative of Riemann-Liouville on time scales, we first introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Then, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and some imbeddings. Finally, as an application, by constructing an appropriate variational setting, using fibering mapping and Nehari manifolds, the existence of weak solutions for a class of fractional boundary value problems on time scales is studied, and a result of the existence of weak solutions for this problem is obtained. |
| format | Article |
| id | doaj-art-4405a35a92994dc69e549464056b9b4a |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-4405a35a92994dc69e549464056b9b4a2025-02-03T06:01:01ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/7149356Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time ScalesXing Hu0Yongkun Li1Department of MathematicsDepartment of MathematicsBy the concept of fractional derivative of Riemann-Liouville on time scales, we first introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Then, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and some imbeddings. Finally, as an application, by constructing an appropriate variational setting, using fibering mapping and Nehari manifolds, the existence of weak solutions for a class of fractional boundary value problems on time scales is studied, and a result of the existence of weak solutions for this problem is obtained.http://dx.doi.org/10.1155/2022/7149356 |
| spellingShingle | Xing Hu Yongkun Li Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales Journal of Function Spaces |
| title | Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales |
| title_full | Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales |
| title_fullStr | Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales |
| title_full_unstemmed | Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales |
| title_short | Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales |
| title_sort | fractional sobolev space on time scales and its application to a fractional boundary value problem on time scales |
| url | http://dx.doi.org/10.1155/2022/7149356 |
| work_keys_str_mv | AT xinghu fractionalsobolevspaceontimescalesanditsapplicationtoafractionalboundaryvalueproblemontimescales AT yongkunli fractionalsobolevspaceontimescalesanditsapplicationtoafractionalboundaryvalueproblemontimescales |