  We show a relation between fractional calculus and fractals, based only on
physical and geometrical considerations. The link has been found in the
physical origins of the power-laws, ruling the evolution of many natural
phenomena, whose long memory and hereditary properties are mathematically
modelled by differential operators of non integer order. Dealing with the
relevant example of a viscous fluid seeping through a fractal shaped porous
medium, we show that, once a physical phenomenon or process takes place on an
underlying fractal geometry, then a power-law naturally comes up in ruling its
evolution, whose order is related to the anomalous dimension of such geometry,
as well as to the model used to describe the physics involved. By linearizing
the non linear dependence of the response of the system at hand to a proper
forcing action then, exploiting the Boltzmann superposition principle, a
fractional differential equation is found, describing the dynamics of the
system itself. The order of such equation is again related to the anomalous
dimension of the underlying geometry.
