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Functions of Mittag-Leffler and Fox: The Pathway Model to Tsallis Statistics and Beck-Cohen Superstatistics | | A.M. Mathai
; H.J. Haubold
; | | Date: |
1 Jun 2009 | | Abstract: | In reaction rate theory, in production-destruction 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
generalized hypergeometric functions, switch to Mittag-Leffler functions and
their generalizations into Wright functions and subsequently into Fox
functions. In this paper, connections are established among generalized
Mittag-Leffler functions, Mathai’s pathway model, Tsallis statistics,
Beck-Cohen superstatistics, and among corresponding entropic measures. The
Mittag-Leffler function, for large values of the parameter, approaches a
power-law. For values of the parameter close to zero, the Mittag-Leffler
function behaves like a stretched exponential. The Mittag-Leffler function is a
generalization of the exponential function and represents a deviation from the
exponential paradigm whenever it shows up in solution of physical problems. The
paper elucidates the relation between analytic representations of the
q-exponential function that is fundamental to Tsallis statistics,
Mittag-Leffler, Wright, and Fox functions, respectively, utilizing
Mellin-Barnes integral representations. | | Source: | arXiv, 0906.0243 | | Services: | Forum | Review | PDF | Favorites | |
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