  We present a set of restrictions on the fractional differential equation
$x^{(\alpha)}(t)=g(x(t))$, $t\geq0$, where $\alpha\in(0,1)$ and $g(0)=0$, that
leads to the existence of an infinity of solutions starting from $x(0)=0$. The
operator $x^{(\alpha)}$ is the Caputo differential operator.
