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# Functions of Mittag-Leffler and Fox: The Pathway Model to Tsallis Statistics and Beck-Cohen Superstatistics

06/2009;

Source: arXiv

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**ABSTRACT:**Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the “slash product,” defined by A(1+&egr;B) =A+&egr;A/B+O(&egr;2). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given.Journal of Mathematical Physics 01/1997; 38(1):484-500. · 1.30 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The paper discusses the solution of a simple kinetic equation of thetype used for the computation of the change of the chemical compositionin stars like the Sun. Starting from the standard form of the kineticequation it is generalized to a fractional kinetic equation and itssolutions in terms of H-functions are obtained. The role of thermonuclearfunctions, which are also represented in terms of G- and H-functions,in such a fractional kinetic equation is emphasized. Results containedin this paper are related to recent investigations of possibleastrophysical solutions of the solar neutrino problem.Astrophysics and Space Science 08/2000; 273(1):53-63. · 2.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In a recent paper, Saxena et al. (Astro Phys. Space Sci. 282 (2002) 281) developed solutions of generalized fractional kinetic equations in terms of Mittag–Leffler functions. The object of the present paper is to derive the solution of further generalized fractional kinetic equations. Their relation to fundamental laws of physics is briefly discussed. Results are obtained in a compact form in terms of generalized Mittag–Leffler functions and a number of representations of these functions, which are widely distributed in the literature, are compiled for the first time.Physica A: Statistical Mechanics and its Applications 06/2004; · 1.68 Impact Factor

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