On maximal regularity for the Cauchy-Dirichlet parabolic problem with fractional time derivative

We prove two maximal regularity results in spaces of continuous and Holder continuous functions, for a linear Cauchy-Dirichlet problem with a fractional time derivative D-t(alpha). This derivative is intended in the sense of Caputo and alpha is taken in (0,2). In case alpha = 1, we obtain maximal regularity results for parabolic problems already known in mathematical literature. (C) 2019 Elsevier Inc. All rights reserved.