Composite continuous time random walks

Rudolf Hilfer ()
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Rudolf Hilfer: Fakultät für Mathematik und Physik (ICP)

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 12, 1-4

Abstract: Abstract Random walks in composite continuous time are introduced. Composite time flow is the product of translational time flow and fractional time flow [see Chem. Phys. 84, 399 (2002)]. The continuum limit of composite continuous time random walks gives a diffusion equation where the infinitesimal generator of time flow is the sum of a first order and a fractional time derivative. The latter is specified as a generalized Riemann-Liouville derivative. Generalized and binomial Mittag-Leffler functions are found as the exact results for waiting time density and mean square displacement.

Date: 2017
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DOI: 10.1140/epjb/e2017-80369-y

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