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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.11884 |
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| _version_ | 1866910832710909952 |
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| author | Loreti, Paola Sforza, Daniela |
| author_facet | Loreti, Paola Sforza, Daniela |
| contents | We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative, addressing key questions such as well-posedness, regularity, and a trace result in appropriate interpolation spaces. Additionally, we explore the duality relationship with the Caputo fractional time derivative. The analysis is based on expanding the solution in terms of Mittag-Leffler functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trace operators for Riemann--Liouville fractional equations Loreti, Paola Sforza, Daniela Analysis of PDEs We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative, addressing key questions such as well-posedness, regularity, and a trace result in appropriate interpolation spaces. Additionally, we explore the duality relationship with the Caputo fractional time derivative. The analysis is based on expanding the solution in terms of Mittag-Leffler functions. |
| title | Trace operators for Riemann--Liouville fractional equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.11884 |