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 (α−1), and our new formula including a parameter (p−1), as well as the Bose–Einstein distribution with a dimensionless chemical potential μ. It can be said that one role of the fractional parameter (p−1) is almost the same as that of chemical potential (μ) as well as that of the parameter (q−1) in the non-extensive approach.