publication . Article . 2015

generalized continuous time random walks master equations and fractional fokker planck equations

C. N. Angstmann; I. C. Donnelly; B. I. Henry; T. A. M. Langlands; P. Straka;
Open Access
  • Published: 07 Jul 2015 Journal: SIAM Journal on Applied Mathematics, volume 75, pages 1,445-1,468 (issn: 0036-1399, eissn: 1095-712X, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
Abstract
Continuous time random walks, which generalize random walks by adding a stochastic time between jumps, provide a useful description of stochastic transport at mesoscopic scales. The continuous time random walk model can accommodate certain features, such as trapping, which are not manifest in the standard macroscopic diffusion equation. The trapping is incorporated through a waiting time density, and a fractional diffusion equation results from a power law waiting time. A generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force. Here we have derived the master equations for cont...
Subjects
free text keywords: Heterogeneous random walk in one dimension, Random walk, Mathematics, Master equation, Anomalous diffusion, Mathematical analysis, Continuous-time random walk, Diffusion equation, Fokker–Planck equation, Fractional calculus
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