Composite continuous time random walks

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 generat...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2017-12, Vol.90 (12), p.1-4, Article 233
Main Author: Hilfer, Rudolf
Format: Article
Language:English
Subjects:
Complex Systems
Condensed Matter Physics
Continuity (mathematics)
Current State and Outlook
Fluid- and Aerodynamics
Physics
Physics and Astronomy
Random walk
Random walk theory
Regular Article
Solid State Physics
Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History
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Summary: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.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2017-80369-y