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Fractional Evolution Equations and Irreversibility

In: Traffic and Granular Flow ’99

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  • R. Hilfer

    (ICA-1, Universität Stuttgart
    Universität Mainz, Institut für Physik)

Abstract

The paper reviews a general theory predicting the general importance of fractional evolution equations. Fractional time evolutions are shown to arise from a microscopic time evolution in a certain long time scaling limit. Fractional time evolutions are generally irreversible. The infinitesimal generators of fractional time evolutions are fractional time derivatives. Evolution equations containing fractional time derivatives are proposed for physical, economical and traffic applications. Regular non-fractional time evolutions emerge as special cases from the results. Also for these regular time evolutions it is found that macroscopic irreversibility arises in the scaling limit.

Suggested Citation

  • R. Hilfer, 2000. "Fractional Evolution Equations and Irreversibility," Springer Books, in: Dirk Helbing & Hans J. Herrmann & Michael Schreckenberg & Dietrich E. Wolf (ed.), Traffic and Granular Flow ’99, pages 215-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59751-0_20
    DOI: 10.1007/978-3-642-59751-0_20
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