On the Properties of the Semigroup Generated by the RL Fractional Integral
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910439217037312 |
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| author | Cheung, Kyan Ka Hin Soh, Ethan Jon Yi |
| author_facet | Cheung, Kyan Ka Hin Soh, Ethan Jon Yi |
| contents | For operators $A$, it is sometimes possible to define $e^{At}$ as an operator in and of itself provided it meets certain regularity conditions. Like $e^{λx}$ for ODEs, this operator is useful for solving PDEs involving the operator $A$. We call the set of $e^{At}$ a semigroup generated by $A$. In this paper, we discuss the properties of semigroups generated by the fractional integral, an operator appearing in PDEs in increasingly many fields, over Bochner-Lebesgue spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Properties of the Semigroup Generated by the RL Fractional Integral Cheung, Kyan Ka Hin Soh, Ethan Jon Yi Functional Analysis For operators $A$, it is sometimes possible to define $e^{At}$ as an operator in and of itself provided it meets certain regularity conditions. Like $e^{λx}$ for ODEs, this operator is useful for solving PDEs involving the operator $A$. We call the set of $e^{At}$ a semigroup generated by $A$. In this paper, we discuss the properties of semigroups generated by the fractional integral, an operator appearing in PDEs in increasingly many fields, over Bochner-Lebesgue spaces. |
| title | On the Properties of the Semigroup Generated by the RL Fractional Integral |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.05265 |