A New Blackbody Radiation Law Based on Fractional Calculus and its
  Application to NASA COBE Data
  By applying fractional calculus to the equation proposed by M. Planck in
1900, 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-extensive
formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a
fractional parameter $(\alpha-1)$, and our new formula including a parameter
$(p-1)$, as well as the Bose-Einstein distribution with a dimensionless
chemical potential $\mu$. It can be said that one role of the fractional
parameter $(p-1)$ is almost the same as that of chemical potential $(\mu)$ as
well as that of the parameter $(q-1)$ in the non-extensive approach.
