On Maximal Regularity for Abstract Parabolic Problems with Fractional Time Derivative

  • Davide GuidettiEmail author


We consider initial value problems for abstract evolution equations with fractional time derivative. Concerning the Caputo derivative \(\mathbb {D}^\alpha u\), we show that certain assumptions, which are known to be sufficient to get a unique solution with a prescribed regularity, are also necessary. So we establish a maximal regularity result. We consider similar problems with the Riemann–Liouville derivative \(\partial ^\alpha u\). Here, we give a complete proof (necessity and sufficiency of the assumptions) of the corresponding maximal regularity results.


Fractional time derivatives Linear evolution equations Maximal regularity 

Mathematics Subject Classification

34K37 34G10 



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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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