Fractons and high-$T_{c}$ superconductivity

We consider the concept of fractons in the context of high-$T_{c}$ superconductivity. These objects, which carry rational or irrational quantum numbers, are classified into universal classes $h$ of particles or quasiparticles which obey specific fractal distribution function. We show that the relaxation time associated to Hall conductivity for the superconducting cuprate systems came to out as $\tau_{H}\propto T^{-2}$. We also consider the pairing of fractons as a mechanism to produce bosonic systems and therefore superconducting states. For that an effective mass obtained from the propagator of a charge-flux system is considered. In this way, some experimental results of infrared studies of the cuprates for the effective mass, $m^*=m_{e}(1+\lambda)$, compared with our effective mass expression, $m_{eff}=m(1+s)$, show us that the dominant factor for interactions came from the spin. Thus spin flutuactions as a mechanism of high-$T_{c}$ superconductivity and fractons as quasiparticles are related. An expression to the low temperature specific heat of a quantum liquid of fractons is also obtained.