2022-05-25T11:10:29Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000178662021-09-02T06:22:23Z1169:1170A new blackbody radiation law based on fractional calculus and its application to NASA COBE dataBiyajima, MinoruMizoguchi, TakuyaSuzuki, Naomichi© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Planck distributionFractional calculusMittag-Leffler functionBose-Einstein distributionNon-extensive approachNASA COBE dataBy 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 CODE 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 nonextensive approach. (C) 2015 Elsevier B.V. All rights reserved.ArticlePHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS. 440:129-138 (2015)ELSEVIER SCIENCE BV2015-12-15engjournal articleAMhttp://hdl.handle.net/10091/00018635https://soar-ir.repo.nii.ac.jp/records/17866https://doi.org/10.1016/j.physa.2015.08.01510.1016/j.physa.2015.08.0150378-4371AA11252758PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS440129138https://soar-ir.repo.nii.ac.jp/record/17866/files/A_new_blackbody_radiation_law_based.pdfapplication/pdf344.6 kB2017-12-15