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  4. Generalized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations

Generalized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations

MMC.
2019;
Volume 6, Number 1
: pp. 58-68
https://doi.org/10.23939/mmc2019.01.058
Received: March 01, 2019
Revised: May 23, 2019
Accepted: May 30, 2019

Math. Model. Comput. Vol.6, No.1, pp.58-68 (2019)

Authors:
  1. P. Kostrobij
  2. B. Markovych
  3. O. Viznovych
  4. I. Zelinska
  5. M. Tokarchuk
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University
5
Lviv Polytechnic National University; Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine

The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo--Maxwell diffusion equation with taking into account the space-time nonlocality are obtained.  Dispersion relations for the Cattaneo--Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found.  The frequency spectrum, phase and group velocities are calculated.  It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.

generalized diffusion equation
nonequilibrium statistical operator
Renyi statistics
multifractal time
spatial fractality
nonlocality of space-time
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