%0 Journal Article 
%A Alvarez, Edgardo
%A Lizama, Carlos
%A Murillo Arcila, Marina
%T Maximal regularity of solutions for the tempered fractional Cauchy problem
%D 2026
%@ 0022-1236

%U http://hdl.handle.net/10498/37336
%X Let $X$ be a Banach space. Given a closed linear operator $A$ defined on $X$ we show that, in vector-valued H\"older spaces $C^{\alpha}(\R,X)\, \, (0<\alpha<1)$,  maximal regularity  for the  abstract Cauchy problem can be characterized solely in terms of a spectral property of the operator $A$, when we equip  the Cauchy problem with the tempered fractional derivative. In particular, we show  that generators of bounded analytic semigroups  admit maximal regularity.
%K Maximal regularity
%K Hölder spaces
%K Abstract Cauchy problem
%K Tempered fractional derivatives
%~ Universidad de Cádiz