@misc{10498/37336,
year = {2026},
url = {http://hdl.handle.net/10498/37336},
abstract = {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.},
publisher = {Elsevier},
keywords = {Maximal regularity},
keywords = {Hölder spaces},
keywords = {Abstract Cauchy problem},
keywords = {Tempered fractional derivatives},
title = {Maximal regularity of solutions for the tempered fractional Cauchy problem},
doi = {10.1016/j.jfa.2025.111196},
author = {Alvarez, Edgardo and Lizama, Carlos and Murillo Arcila, Marina},
}