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Axioms 2015, 4(3), 385-399; doi:10.3390/axioms4030385

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

Indian Statistical Institute(ISI), Chennai CIT Campus, Taramani, Chennai 600113, India
Academic Editor: Hans J. Haubold
Received: 15 July 2015 / Revised: 10 August 2015 / Accepted: 10 August 2015 / Published: 26 August 2015
View Full-Text   |   Download PDF [567 KB, uploaded 26 August 2015]   |  

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 of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thicker- or thinner-tailed models associated with a gamma-type distribution as a limiting case of the pathway operator. Applications of this extended gamma model in statistical mechanics, input-output models, solar spectral irradiance modeling, etc., are established. View Full-Text
Keywords: fractional integrals; statistical distributions; Bessel function; gamma model fractional integrals; statistical distributions; Bessel function; gamma model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sebastian, N. Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines. Axioms 2015, 4, 385-399.

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