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

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 $q\to 1$. 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.

arXiv admin note: text overlap with arXiv:0705.0148 by other authors

References in corpus (3)

• Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy
• Coarse-grained distributions and superstatistics
• Stretched exponentials from superstatistics