  We introduce the notion of fractal index associated with the universal class
$h$ of particles or quasiparticles, termed fractons, which obey specific
fractal statistics. A connection between fractons and conformal field
theory(CFT)-quasiparticles is established taking into account the central
charge $c[\nu]$ and the particle-hole duality
$\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the
statistical parameter. In this way, we derive the Fermi velocity in terms of
the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$
which labelled the universal classes of particles and the conformal anomaly are
therefore related. Following another route, we also established a connection
between Rogers dilogarithm function, Farey series of rational numbers and the
Hausdorff dimension.
