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Bibliographic Details
Main Authors: Kostrobij, P., Tokarchuk, M., Markovych, B., Ryzha, I.
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2008.10645
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author Kostrobij, P.
Tokarchuk, M.
Markovych, B.
Ryzha, I.
author_facet Kostrobij, P.
Tokarchuk, M.
Markovych, B.
Ryzha, I.
contents Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion $D^{αα'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{αα'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in fractional time and space derivatives has been obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo--Maxwell diffusion equation in fractional time and space derivatives have been performed. Numerical calculations of the phase and group velocities with change of values of characteristic relaxation time, diffusion coefficient and indexes of temporal $ξ$ and spatial $α$ fractality have been carried out.
format Preprint
id arxiv_https___arxiv_org_abs_2008_10645
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Generalized diffusion equation with nonlocality of space-time: analytical and numerical analysis
Kostrobij, P.
Tokarchuk, M.
Markovych, B.
Ryzha, I.
Statistical Mechanics
35A99, 35B99
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion $D^{αα'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{αα'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in fractional time and space derivatives has been obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo--Maxwell diffusion equation in fractional time and space derivatives have been performed. Numerical calculations of the phase and group velocities with change of values of characteristic relaxation time, diffusion coefficient and indexes of temporal $ξ$ and spatial $α$ fractality have been carried out.
title Generalized diffusion equation with nonlocality of space-time: analytical and numerical analysis
topic Statistical Mechanics
35A99, 35B99
url https://arxiv.org/abs/2008.10645