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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
Minoru Biyajima, Takuya Mizoguchi, Naomichi Suzuki
To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, . It is satisfied with the stationary solution…
The effects of the chemical potential in a BE distribution and the fractional parameter in a distribution with Mittag-Leffler function
Minoru Biyajima, Takuya Mizoguchi, Naomichi Suzuki
The fractional Planck distribution is calculated by applying the Caputo fractional derivative with order () to the equation proposed by Planck in 1900. In addition, the…
A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data
Minoru Biyajima, Takuya Mizoguchi, Naomichi Suzuki
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…
Analysis of residual spectra and the monopole spectrum for 3 K blackbody radiation by means of non-extensive thermostatistics
Minoru Biyajima, Takuya Mizoguchi
We analyze residual spectra of 3 K blackbody radiation (CMB) using non-extensive thermostatistics with a parameter q-1. The limits of |q-1|<1.2x10^{-5} and the temperature fluctuat…
Analysis of distribution of cosmic microwave background photon in terms of non-extensive statistics and formulas with temperature fluctuation
M. Biyajima, M. Kaneyama, Y. Kurashima +2
To take into account the temperature fluctuation in the Planck distribution, we calculate convolution integral with several probability distributions. Using these formula as well t…