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Towards the formulation of a nonlinear fractional extended irreversible thermodynamics

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Acta Physica Hungarica

Abstract

For the class of all discrete two-velocity models of the nonlinear Boltzmann equation consistent with theH-theorem an exact representation of the corresponding nonlinear constitutive equation will be derived. Applying the fractional calculus we derive, in addition, the nonlinear fractional Boltzmann equation as the starting point for the formulation of a nonlinear fractional constitutive equation which relates the densities and fluxes through an integro-differential equation. Linearization leads to the fractional version of Cattaneo's constitutive law. The model presented here may be regarded as a first step, towards the formulation of a fractional extended irreversible thermodynamics.

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Authors and Affiliations

  1. Faculty for Mathematics and Natural Sciences, University of Ulm, D-79, Ulm, FRG

    T. F. Nonnenmacher & D. J. F. Nonnenmacher

Authors
  1. T. F. Nonnenmacher
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  2. D. J. F. Nonnenmacher
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Dedicated to Prof. I. Gyarmati on his 60th birthday

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Nonnenmacher, T.F., Nonnenmacher, D.J.F. Towards the formulation of a nonlinear fractional extended irreversible thermodynamics. Acta Physica Hungarica 66, 145–154 (1989). https://doi.org/10.1007/BF03155787

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  • DOI: https://doi.org/10.1007/BF03155787

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