  Using known estimates for the kaon--antikaon transitions, the mean lifetime
of the muon and the mean lifetime of the tau, we place new and stronger
constraints on the scales of the multi-fractional theories with weighted and
$q$-derivatives. These scenarios reproduce a quantum-gravity regime where
fields live on a continuous spacetime with a scale-dependent Hausdorff
dimension. In the case with weighted derivatives, constraints from the muon
lifetime are various orders of magnitude stronger than those from the tau
lifetime and the kaon--antikaon transitions. The characteristic energy scale of
the theory cannot be greater than $E_*>3\times 10^2\,{\rm TeV}$, and is
tightened to $E_*>9\times 10^{8}\,{\rm TeV}$ for the typical value $\alpha=1/2$
of the fractional exponents in the spacetime measure. We also find an upper
bound $d_{\rm H}<2.9$ on the spacetime Hausdorff dimension in the ultraviolet.
In the case with $q$-derivatives, the strongest bound comes from the tau
lifetime, but it is about 10 orders of magnitude weaker than for the theory
with weighted derivatives.
