A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data

摘要

By applying fractional calculus to the equation proposed by M. Planck in1900, we obtain a new blackbody radiation law described by a Mittag-Leffler(ML) function. We have analyzed NASA COBE data by means of a non-extensiveformula with a parameter $(q-1)$, a formula proposed by Ertik et al. with afractional parameter $(\alpha-1)$, and our new formula including a parameter$(p-1)$, as well as the Bose-Einstein distribution with a dimensionlesschemical potential $\mu$. It can be said that one role of the fractionalparameter $(p-1)$ is almost the same as that of chemical potential $(\mu)$ aswell as that of the parameter $(q-1)$ in the non-extensive approach.