THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Xiao-Jun Yang

,

Yu-Mei Pan

,

Feng Xu

ANOMALOUS DIFFUSION MODELS WITH RESPECT TO MONOTONE INCREASING FUNCTIONS

ABSTRACT
In this article we propose the anomalous diffusion models with respect to mono-tone increasing functions. The Riesz-type fractional order derivatives operators with respect to power-law function are considered based on the extended work of Riesz. Two models for the anomalous diffusion processes are given to describe the special behaviors in the complex media
KEYWORDS
anomalous diffusion, Riesz fractional derivative, Riesz-type fractional derivative with respect to monotone increasing function, Riesz-type fractional derivative with respect to power-law function
PAPER SUBMITTED: 2021-08-12
PAPER REVISED: 2021-08-26
PAPER ACCEPTED: 2021-09-02
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202009Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1009 - 1016]
REFERENCES
  1. Fick, A., Ueber Diffusion, Annalen der Physik, 170 (1855), 1, pp. 59-86
  2. Fick, A. V., On Liquid Diffusion, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10 (1855), 63, pp. 30-39
  3. Richardson, L. F., Atmospheric Diffusion Shown on a Distance-Neighbour Graph, Proceedings of the Royal Society A, 110 (1926), 756, pp. 709-737
  4. Bouchaud, J. P., Georges, A., Anomalous Diffusion in Disordered Media: Statistical Mechanisms, Mod-els and Physical Applications, Physics Reports, 195 (1990), 4-5, pp. 127-293
  5. Alcazar-Cano, N., Delgado-Buscalioni, R., A General Phenomenological Relation for the Subdiffusive Exponent of Anomalous Diffusion in Disordered Media, Soft Matter, 14 (2018), 48, pp. 9937-9949
  6. Metzler, R., et al., Anomalous Diffusion Models and Their Properties: Non-stationarity, non-ergodicity, and ageing at the centenary of single particle Tracking, Physical Chemistry Chemical Physics, 16 (2014), 44, pp. 24128-24164
  7. Knackstedt, M. A., et al., Diffusion in Model Disordered Media, Physical Review Letters, 75 (1995), 4, pp. 653-656
  8. Jeon, J. H., et al., Anomalous Diffusion of Phospholipids and Cholesterols in a Lipid Bilayer and Its Or-igins, Physical Review Letters, 109 (2012), 18, ID188103-5
  9. Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84 (2016), 1, pp. 3-7
  10. Chen, W., et al., Anomalous Diffusion Modeling by Fractal and Fractional Derivatives, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1754-1758
  11. Riesz, M., L'intégrale de Riemann-Liouville et le Problème de Cauchy, Acta Mathematica, 81 (1949), Dec., pp. 1-222
  12. Yang, X. J., General Fractional Derivatives: Theory, Methods and Applications, CRC Press, Boka Ra-ton, Fla., USA, 2019
  13. Samko, S. G., et al., Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993
  14. Yang, X. J., et al., General Fractional Derivatives with Applications in Viscoelasticity, Academic Press, New York, USA, 2020
  15. Herrmann, R., Fractional Calculus: An Introduction For Physicists, World Scientific, Singapore, 2014
  16. Fernandez, A., et al., On the Fractional Laplacian of a Function with Respect to Another Function, On-line first, hal.archives-ouvertes.fr/hal-03318401, 2021
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Anomalous diffusion models with respect to monotone increasing functions

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence