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EnglishWe consider initial value problems for abstract evolution equa- tions with fractional time derivative. Concerning the Caputo derivative Dαu, we show that certain assumptions, which are known to be suf- ficient to get a unique solution with a prescribed regularity, are also necessary. So we establish a maximal regularity result. We consider sim- ilar problems with the Riemann–Liouville derivative ∂αu. Here, we give a complete proof (necessity and sufficiency of the assumptions) of the corresponding maximal regularity results.
| Titolo: | On maximal regularity for abstract parabolic problems with fractional time derivative | |
| Autore/i: | Guidetti, D | |
| Autore/i Unibo: | ||
| Anno: | 2019 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00009-019-1309-y | |
| Abstract: | We consider initial value problems for abstract evolution equa- tions with fractional time derivative. Concerning the Caputo derivative Dαu, we show that certain assumptions, which are known to be suf- ficient to get a unique solution with a prescribed regularity, are also necessary. So we establish a maximal regularity result. We consider sim- ilar problems with the Riemann–Liouville derivative ∂αu. Here, we give a complete proof (necessity and sufficiency of the assumptions) of the corresponding maximal regularity results. | |
| Data stato definitivo: | 2020-02-19T16:11:52Z | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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