Eur. Phys. J. B (2017) 90: 233
https://doi.org/10.1140/epjb/e2017-80369-y

Regular Article

Composite continuous time random walks^★

Fakultät für Mathematik und Physik (ICP), Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany

^a e-mail: r.hilfer@icp.uni-stuttgart.de

Received: 20 June 2017
Published online: 4 December 2017

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.