A Unified Grand Canonical Description of The Nonextensive   Thermostatistics of The Quantum Gases: Fractal and Fractional Approach
  In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive standard thermostatistical relations of the Bose and Fermi systems are recovered. 
F.Buyukkilic (1),D.Demirhan (1);((1)Department of Physics, Faculty of   Science, Ege University, Bornova, Izmir, Turkey)