A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data

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.

References in corpus (3)

• Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -
• Analysis of residual spectra and the monopole spectrum for 3 K blackbody radiation by means of non-extensive thermostatistics
• Monte Carlo Study on Distortion of the Space-Dimension in COBE Monopole Data

Cited by in corpus (3)

• Piecewise linear approximate solution of fractional order non-stiff and stiff differential-algebraic equations by orthogonal hybrid functions
• New orthogonal hybrid function based numerical method to solve system of fractional order differential equations
• 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