  The fractional Planck distribution is calculated by applying the Caputo
fractional derivative with order $p$ ($p > 0$) to the equation proposed by
Planck in 1900. In addition, the integral representation of the Mittag--Leffler
function is employed to obtain a new formula for the fractional BE
distribution, which is then used to analyze the NASA COBE monopole data. Based
on this analysis, an identity $p\simeq e^{-\mu}$ is found, where $\mu$ is the
dimensionless constant chemical potential that was introduced to the BE
distribution by the NASA COBE collaboration.
