||A new blackbody radiation law based on fractional calculus and its application to NASA COBE data
Biyajima, Minoru ,
Mizoguchi, TakuyaSuzuki, Naomichi
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
138 , 2015-12-15 , ELSEVIER SCIENCE BV
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 CODE 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 nonextensive approach. (C) 2015 Elsevier B.V. All rights reserved.