On a Generalization of One-Dimensional Kinetics

Vladimir V. Uchaikin, Renat T. Sibatov and Dmitry N. Bezbatko
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Vladimir V. Uchaikin: Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432017, Russia
Renat T. Sibatov: Moscow Institute of Physics and Technology, Moscow 141701, Russia
Dmitry N. Bezbatko: Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432017, Russia

Mathematics, 2021, vol. 9, issue 11, 1-18

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.

Keywords: random walk; telegraph equation; fractional material derivative; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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