  An autonomous Caputo fractional differential equation of order
$\alpha\in(0,1)$ in $\mathbb{R}^d$ whose vector field satisfies a global
Lipschitz condition is shown to generate a semi-dynamical system in the
function space $\mathfrak{C}$ of continuous functions $f:\R^+\rightarrow \R^d$
with the topology uniform convergence on compact subsets.
  This contrasts with a recent result of Cong \& Tuan \cite{cong}, which showed
that such equations do not, in general, generate a dynamical system on the
space $\mathbb{R}^d$.
