  Time-dependent fractional-derivative problems $D_t^\delta u + Au = f$ are
considered, where $D_t^\delta$ is a Caputo fractional derivative of order
$\delta\in (0,1)\cup (1,2)$ and~$A$ is a classical elliptic operator, and
appropriate boundary and initial conditions are applied. The regularity of
solutions to this class of problems is discussed, and it is shown that assuming
more regularity than is generally true---as many researchers do---places a
surprisingly severe restriction on the problem.
