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- Title
On a Generalization of One-Dimensional Kinetics.
- Authors
Uchaikin, Vladimir V.; Sibatov, Renat T.; Bezbatko, Dmitry N.
- Abstract
One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.
- Subjects
DISTRIBUTION (Probability theory); GENERALIZATION; MONTE Carlo method; RANDOM walks; TRAILS
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 11, p1264
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9111264