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

Author

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  • Biyajima, Minoru
  • Mizoguchi, Takuya
  • Suzuki, Naomichi

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.

Suggested Citation

  • Biyajima, Minoru & Mizoguchi, Takuya & Suzuki, Naomichi, 2015. "A new blackbody radiation law based on fractional calculus and its application to NASA COBE data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 129-138.
    • Handle: RePEc:eee:phsmap:v:440:y:2015:i:c:p:129-138
    DOI: 10.1016/j.physa.2015.08.015
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    Cited by:

    1. Alexander Apelblat, 2020. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach," Mathematics, MDPI, vol. 8(5), pages 1-22, April.

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