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

On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric