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Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
Enrico Scalas1, Rudolf Gorenflo, Francesco Mainardi
1Department of Advanced Sciences and Technologies, East Piedmont University, Corso Borsalino 54, I-15100 Alessandria, Italy. scalas@unipmn.it
Abstract:
A detailed study is presented for a large class of uncoupled continuous-time random walks. The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed. Finally, some common objections found in the literature are thoroughly reviewed.