  The aim of this work is to show a non-sharp quantitative stability version of
the fractional isocapacitary inequality. In particular, we provide a lower
bound for the isocapacitary deficit in terms of the Fraenkel asymmetry. In
addition, we provide the asymptotic behaviour of the $s$-fractional capacity
when $s$ goes to $1$ and the stability of our estimate with respect to the
parameter $s$.
