@article{oai:soar-ir.repo.nii.ac.jp:00019994,
 author = {Biyajima, Minoru and Mizoguchi, Takuya and Suzuki, Naomichi},
 issue = {1},
 journal = {Journal of Physics: Conference Series},
 month = {Feb},
 note = {To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, df/dx = −f − f 2. It is satisfied with the stationary solution, f(x) = 1/(e x + μ − 1), of the Kompaneets equation, where μ is the constant chemical potential. Setting R = 1/f, we obtain a linear differential equation for R. Then, the Caputo fractional derivative of order p (p > 0) is introduced in place of the derivative of x, and fractional BE distribution is obtained, where function e x is replaced by the Mittag–Leffler (ML) function Ep(x p ). Using the integral representation of the ML function, we obtain a new formula. Based on the analysis of the NASA COBE monopole data, an identity p sime e −μ is found., Article, Journal of Physics: Conference Series. 936(1):12082(2018)},
 title = {An analytic relation between the fractional parameter in the Mittag–Leffler function and the chemical potential in the Bose–Einstein distribution through the analysis of the NASA COBE monopole data},
 volume = {936},
 year = {2018}
}