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.
On maximal regularity for abstract parabolic problems with fractional time derivative / Guidetti, D. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 16:(2019), pp. 40.39-40.64. [10.1007/s00009-019-1309-y]
On maximal regularity for abstract parabolic problems with fractional time derivative
Guidetti, D
2019
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.