  Over the recent decades, diverse formalisms have emerged that are adopted to
approach complex systems. Amongst those, we may quote the q-calculus in
Tsallis' version of Non-Extensive Statistics with its undeniable success
whenever applied to a wide class of different systems; Kaniadakis' approach,
based on the compatibility between relativity and thermodynamics; Fractional
Calculus (FC), that deals with the dynamics of anomalous transport and other
natural phenomena, and also some local versions of FC that claim to be able to
study fractal and multifractal spaces and to describe dynamics in these spaces
by means of fractional differential equations.
  The question we might ask is whether or not there are common aspects that
connect these alternative approaches. In this short communication, we discuss a
possible relationship between q-deformed algebras in two different contexts of
Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis'
scenario, with local form of fractional-derivative operators defined in fractal
media, the so-called Hausdorff derivatives, mapped into a continuous medium
with a fractal measure. This connection opens up new perspectives for theories
that satisfactorily describe the dynamics for the transport in media with
fractal metrics, such as porous or granular media. Possible connections with
other alternative definitions of FC are also contempled. Insights on complexity
connected to concepts like coarse-grained space-time and physics in general are
pointed out.
