Fractional statistical dynamics and fractional kinetics

Abstract

We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in terms of a non-linear Vlasov-type kinetic equation. As an application we study the intermittency of the fractional mesoscopic dynamics.

Key words: Configuration space, Caputo derivative, Vlasov-type kinetic equation, correlation functions, Poisson flow.

Full Text

Article Information

Title	Fractional statistical dynamics and fractional kinetics
Source	Methods Funct. Anal. Topology, Vol. 22 (2016), no. 3, 197-209
MathSciNet	MR3554648
zbMATH	06742106
Milestones	Received 17/03/2016; Revised 03/04/2016
Copyright	The Author(s) 2016 (CC BY-SA)

Authors Information

José Luís da Silva
CCM, University of Madeira, Campus da Penteada, 9020-105 Funchal, Portugal

Anatoly N. Kochubei
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Yuri Kondratiev
Department of Mathematics, University of Bielefeld, D-33615 Bielefeld, Germany

Citation Example

José Luís da Silva, Anatoly N. Kochubei, and Yuri Kondratiev, Fractional statistical dynamics and fractional kinetics, Methods Funct. Anal. Topology 22 (2016), no. 3, 197-209.

BibTex

@article {MFAT890,
    AUTHOR = {da Silva, José Luís and Kochubei, Anatoly N. and Kondratiev, Yuri},
     TITLE = {Fractional statistical dynamics and fractional kinetics},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {197-209},
      ISSN = {1029-3531},
  MRNUMBER = {MR3554648},
 ZBLNUMBER = {06742106},
       URL = {http://mfat.imath.kiev.ua/article/?id=890},
}

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