  Using a temporally weighted norm we first establish a result on the global
existence and uniqueness of solutions for Caputo fractional stochastic
differential equations of order $\alpha\in(\frac{1}{2},1)$ whose coefficients
satisfy a standard Lipschitz condition. For this class of systems we then show
that the asymptotic distance between two distinct solutions is greater than
$t^{-\frac{1-\alpha}{2\alpha}-\eps}$ as $t \to \infty$ for any $\eps>0$. As a
consequence, the mean square Lyapunov exponent of an arbitrary non-trivial
solution of a bounded linear Caputo fractional stochastic differential equation
is always non-negative.
