  We prove two maximal regularity results in spaces of continuous and H\"older
continuous functions, for a mixed linear Cauchy-Dirichlet problem with a
fractional time derivative $\mathbb{D}_t^\alpha$. 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 mixed parabolic problems already known
in mathematica literature.
