  We consider fractional differential equations of order $\alpha \in (0,1)$ for
functions of one independent variable $t\in (0,\infty)$ with the
Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise
estimate for the order of growth of $\alpha$-entire solutions is given. An
analog of the Frobenius method for systems with regular singularity is
developed. For a model example of an equation with a kind of an irregular
singularity, a series for a formal solution is shown to be convergent for $t>0$
(if $\alpha$ is an irrational number poorly approximated by rational ones) but
divergent in the distribution sense.
