A fractional mathematical approach to the distribution functions of quantum gases: Cosmic Microwave Background Radiation problem is revisited

Efforts on the fundamentals of the nonextensive thermostatistical formulations of the realistic description of the physical systems have always been underway. In this context, the quantum systems of bosons and fermions are taken into consideration as g-ons. A new formalism of the unified distribution functions has been introduced using a fractional mathematical approach. With the purpose of verification of the theory, blackbody radiation problem has been investigated by making use of the generalized fractional Planck’s distribution. In this context, the observed Cosmic Microwave Background Radiation (CMBR) energy density could be obtained exactly within nonextensive thermostatistical approach for the value α=0.999983 of the order of the fractional derivative and for the blackbody temperature T=2.72818 K.