Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and its Applications in Various Disciplines

TL;DR

This paper develops a generalized gamma Bessel model using fractional calculus, explores its properties, and demonstrates its applications across disciplines like statistical mechanics and solar irradiance modeling.

Contribution

It introduces a new limiting approach to the generalized gamma Bessel model via fractional calculus, expanding the class of extended densities for various applications.

Findings

Extended gamma models with thicker or thinner tails are derived as limits.

Applications in statistical mechanics and solar irradiance are demonstrated.

Almost all extended densities for pathway parameter q are characterized.

Abstract

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one can list out almost all the extended densities for the pathway parameter $q < 1$ and $q \rightarrow 1$. Here we bring out the idea of thicker or thinner tailed models associated with a gamma type distribution as a limiting case of pathway operator. Applications of this extended gamma model in Statistical Mechanics, input-output models, and solar spectral irradiance modeling etc are established.