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On a Generalization of One-Dimensional Kinetics

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vladimir V. Uchaikin & Renat T. Sibatov & Dmitry N. Bezbatko, 2021. "On a Generalization of One-Dimensional Kinetics," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1264-:d:566501
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    References listed on IDEAS

    as
    1. Shlesinger, Michael F. & Klafter, Joseph & J. West, Bruce, 1986. "Levy walks with applications to turbulence and chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 212-218.
    2. Renat T. Sibatov, 2020. "Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    Full references (including those not matched with items on IDEAS)

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