{"paper":{"title":"An analytic relation between the fractional parameter in the Mittag-Leffler function and the chemical potential in the Bose-Einstein distribution through the analysis of the NASA COBE monopole data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","hep-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Minoru Biyajima, Naomichi Suzuki, Takuya Mizoguchi","submitted_at":"2017-09-24T15:41:13Z","abstract_excerpt":"To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, $df/dx =-f-f^2$. It is satisfied with the stationary solution, $f(x)=1/(e^{x+\\mu}-1)$, of the Kompaneets equation, where $\\mu$ is the constant chemical potential. Setting $R=1/f$, we obtain a linear differential equation for $R$. Then, the Caputo fractional derivative of order $p$ ($p>0$) is introduced in place of the derivative of $x$, and fractional BE distribution is obtained, where function ${\\rm e}^x$ is replaced by the Mittag-Leffler (ML) function $E_p(x^p)$. Using the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08212","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}