Composite continuous time random walks

Regular Article
Part of the following topical collections:
  1. Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook

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.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Fakultät für Mathematik und Physik (ICP)Universität StuttgartGermany

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