Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 491, Issue -, Pages 1001-1013Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2017.09.101
Keywords
Anomalous diffusion; Conformable derivative; Gauss kernel; Mean square displacement; Error function
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Funding
- National Natural Science Foundation of China [51674266, 11371364]
- State Key Research Development Program of China [2016YFC0600704]
- Specialized Research Fund for the Doctoral Program of Higher Education [20130023110017]
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By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed. (C) 2017 Elsevier B.V. All rights reserved.
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