Mittag-Leffler Functions to Pathway Model to Tsallis Statistics

TL;DR

This paper explores the connections between Mittag-Leffler functions, pathway models, and Tsallis statistics, highlighting their roles in fractional calculus applications in reaction rate and reaction-diffusion models.

Contribution

It establishes new links among generalized Mittag-Leffler functions, pathway models, Tsallis statistics, and related entropic measures, expanding the theoretical framework.

Findings

Mittag-Leffler functions relate to pathway models and Tsallis statistics.

Connections among generalized Mittag-Leffler functions and entropic measures are established.

The work enhances understanding of fractional calculus solutions in physical models.

Abstract

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their generalizations. When fractional calculus enters into the picture the solutions of these problems, usually available in terms of hypergeometric functions, G and H-functions, switch to Mittag-Leffler functions and their generalizations into Wright functions. In this paper, connections are established among generalized Mittag-Leffler functions, pathway model, Tsallis statistics, superstatisitcs and power law, and among the corresponding entropic measures.