%0 Journal Article %1 Hilfer2017 %A Hilfer, Rudolf %D 2017 %J The European Physical Journal B %K %N 12 %P 233 %R 10.1140/epjb/e2017-80369-y %T Composite continuous time random walks %U https://doi.org/10.1140/epjb/e2017-80369-y %V 90 %X 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.

@article{Hilfer2017, 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.}, added-at = {2023-09-11T23:13:13.000+0200}, author = {Hilfer, Rudolf}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2afe93d2e29346f30c2cafcab39426adb/icp_bib}, day = 04, doi = {10.1140/epjb/e2017-80369-y}, interhash = {d6cde9149fbb76bf7d2868af029a9bb0}, intrahash = {afe93d2e29346f30c2cafcab39426adb}, issn = {1434-6036}, journal = {The European Physical Journal B}, keywords = {}, month = dec, number = 12, pages = 233, timestamp = {2023-09-11T23:13:13.000+0200}, title = {Composite continuous time random walks}, url = {https://doi.org/10.1140/epjb/e2017-80369-y}, volume = 90, year = 2017 }