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A new blackbody radiation law based on fractional calculus and its application to NASA COBE data

2015; Elsevier BV; Volume: 440; Linguagem: Inglês

10.1016/j.physa.2015.08.015

1873-2119

M. Biyajima, Takuya Mizoguchi, Naomichi Suzuki,

Advanced Mathematical Theories and Applications

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.