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Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method

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  • Kostrobij, P.P.
  • Markovych, B.M.
  • Viznovych, O.V.
  • Tokarchuk, M.V.

Abstract

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev’s nonequilibrium statistical operator (NSO) method within Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.

Suggested Citation

  • Kostrobij, P.P. & Markovych, B.M. & Viznovych, O.V. & Tokarchuk, M.V., 2019. "Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 63-70.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:63-70
    DOI: 10.1016/j.physa.2018.09.051
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    References listed on IDEAS

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    1. Qi, Haitao & Jiang, Xiaoyun, 2011. "Solutions of the space-time fractional Cattaneo diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1876-1883.
    2. Markiv, B.B. & Tokarchuk, R.M. & Kostrobij, P.P. & Tokarchuk, M.V., 2011. "Nonequilibrium statistical operator method in Renyi statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 785-791.
    3. Sun, HongGuang & Chen, Wen & Li, Changpin & Chen, YangQuan, 2010. "Fractional differential models for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2719-2724.
    4. Nigmatullin, R.R., 2006. "‘Fractional’ kinetic equations and ‘universal’ decoupling of a memory function in mesoscale region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 282-298.
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