Mittag-Leffler functions to pathway model to Tsallis statistics

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, superstatistics and power law, and among the corresponding entropic measures.