  Fractons are anyons classified into equivalence classes and they obey a
specific fractal statistics. The equivalence classes are labeled by a fractal
parameter or Hausdorff dimension $h$. We consider this approach in the context
of the Fractional Quantum Hall Effect (FQHE) and the concept of duality between
such classes, defined by $\tilde{h}=3-h$ shows us that the filling factors for
which the FQHE were observed just appear into these classes. A connection
between equivalence classes $h$ and the modular group for the quantum phase
transitions of the FQHE is also obtained. A $\beta-$function is defined for a
complex conductivity which embodies the classes $h$. The thermodynamics is also
considered for a gas of fractons $(h,\nu)$ with a constant density of states
and an exact equation of state is obtained at low-temperature and low-density
limits. We also prove that the Farey sequences for rational numbers can be
expressed in terms of the equivalence classes $h$.
