Maximal Regularity of Solutions for the Tempered Fractional Cauchy Problem

Let X be a Banach space. Given a closed linear operator A defined on X we show that, in vector-valued Hölder spaces Cα(R,X)(0<α<1)[jls-end-space/], 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. © 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.