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
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/729129
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