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

Minoru Biyajima, Takuya Mizoguchi and Naomichi Suzuki

Physica A: Statistical Mechanics and its Applications, 2015, vol. 440, issue C, 129-138

Abstract: 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.

Keywords: Planck distribution; Fractional calculus; Mittag-Leffler function; Bose–Einstein distribution; Non-extensive approach; NASA COBE data (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:440:y:2015:i:c:p:129-138

DOI: 10.1016/j.physa.2015.08.015

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