In general, round-off errors have a relevant impact when either

1) trying to solve very ill conditioned linear systems

2) trying to achieve relative errors barely larger than the machine accuracy (one should not try to achieve less :-)) )

I am not an expert in FDEs, but these two general concepts should apply all the same. Therefore, as long as the linear system one gets have a condition number that is significantly smaller than the reciprocal of the machine accuracy AND the accuracy goals are not excessively ambitious, I would not expect an excessive impact of round-off on the numerical solutions of FDEs.

You can always perturb your initial conditions with some random noise say of magnitude 1e-15. You solve the differential equations and measure the deviations between the different solution. For each perturbation you get an "amplification factor". The largest amplification factor across all possible (small) perturbations is called the absolute condition number, see http://pi.unl.edu/~s-bbockel1/847-notes/Absolute_condition.html. Doing this for a few examples is not a proof but may give you a good idea or starting point...