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

TL;DR

This paper introduces a novel blackbody radiation law derived using fractional calculus, modeled by a Mittag-Leffler function, and applies it to NASA COBE data to compare with existing models.

Contribution

It presents a new blackbody radiation law based on fractional calculus and demonstrates its application to real astrophysical data, comparing it with established models.

Findings

The new law fits NASA COBE data effectively.

The fractional parameter acts similarly to chemical potential.

The model offers an alternative to non-extensive and Bose-Einstein approaches.

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.