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

DOI10.1016/J.PHYSA.2015.08.015zbMATH Open1400.82007arXiv1503.06010OpenAlexW1657301377MaRDI QIDQ1618847

T. Mizoguchi, N. Suzuki, Minoru Biyajima

Publication date: 13 November 2018

Published in: Physica A (Search for Journal in Brave)

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 $(alpha-1)$, 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 non-extensive approach.

Full work available at URL: https://arxiv.org/abs/1503.06010

zbMATH Keywords

Mittag-Leffler functionfractional calculusBose-Einstein distributionNASA COBE datanon-extensive approachPlanck distribution

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Fractional ordinary differential equations (34A08)

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