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

Research paper by Davide Guidetti

Indexed on: 16 Jul '18Published on: 16 Jul '18Published in: arXiv - Mathematics - Analysis of PDEs

#### Abstract

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.