Composite continuous time random walks★
Fakultät für Mathematik und Physik (ICP),
70569 Stuttgart, Germany
a e-mail: email@example.com
Published online: 4 December 2017
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2017