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Variable-order fractional diffusion: Physical interpretation and simulation within the multiple trapping model

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  • Sibatov, Renat T.
  • L'vov, Pavel E.
  • Sun, HongGuang

Abstract

The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between localized and mobile particles is satisfied. The variable order anomalous diffusion equations under consideration can be applied to the description of transient subdiffusion in inhomogeneous materials, the order of which depends on the considered spatial and/or time scale. Examples of numerical solutions for different situations are demonstrated. Considering variable-order fractional drift, we calculate and analyze the transient current curves of the time-of-flight method for samples with varying density of localized states.

Suggested Citation

  • Sibatov, Renat T. & L'vov, Pavel E. & Sun, HongGuang, 2024. "Variable-order fractional diffusion: Physical interpretation and simulation within the multiple trapping model," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    • Handle: RePEc:eee:apmaco:v:482:y:2024:i:c:s0096300324004211
    DOI: 10.1016/j.amc.2024.128960
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    3. Renat T. Sibatov, 2019. "Anomalous Grain Boundary Diffusion: Fractional Calculus Approach," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-9, January.
    4. Straka, Peter, 2018. "Variable order fractional Fokker–Planck equations derived from Continuous Time Random Walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 451-463.
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