Erdélyi-Kober Fractional Calculus and Neutrino Physics

What is it about?

This research presents an in-depth analysis of Erdélyi-Kober fractional integrals and derivatives from a statistical perspective, inspired by the study of solar neutrino physics. It starts by exploring the application of diffusion entropy analysis to solar neutrino data from the Super-Kamiokande experiment, leading to generalizations of entropy (entropic pathway) and diffusion (anomalous diffusion). The work extends these concepts to describe the statistical density of products and ratios of various types of random variables, showing that these can be represented through Erdélyi-Kober fractional integrals. Different chapters detail these fractional integrals and their applications in real scalar, matrix-variate cases, and complex domains, covering both theoretical formulations and physical interpretations.

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Photo by Bozhin Karaivanov on Unsplash

Photo by Bozhin Karaivanov on Unsplash

Why is it important?

Understanding Erdélyi-Kober fractional calculus is crucial for advancing mathematical physics, particularly in areas where traditional models of diffusion and entropy fail to accurately describe complex physical phenomena. This research contributes to a deeper comprehension of the statistical mechanics underpinning neutrino physics and other areas where non-traditional, fractional calculus approaches offer more accurate models. The implications extend beyond neutrino physics, potentially affecting the modeling and analysis in various fields of science and engineering where understanding complex diffusion processes and their statistical descriptions are necessary. KEY TAKEAWAY: This research produces advances in fractional calculus, enriching neutrino physics modeling.