  In this work we present a bag-type model within a non-extensive statistics
applied to the description of the properties of a hadronic system with an
underlying fractal structure. The non-extensive ideal gas inside the bag is
determined by the grand canonical partition function from which pressure,
energy and particle density as well as temperature and chemical potential are
obtained for the hadronic system. These quantities are studied in the
approximation of fixed mass for all bag constituents but also for discrete and
continuum masses. In all cases, the freeze-out line, corresponding to the
energy per particle equal to 1 GeV and the lines corresponding to a fractal
structure inside the proton volume are obtained. Finally, the pressure on the
bag surface of the proton is calculated and the resulting value $(0.135\, {\rm
GeV})^4$ obtained.
