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Stochastic Representation and Monte Carlo Simulation for Multiterm Time‐Fractional Diffusion Equation

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  • Longjin Lv
  • Luna Wang

Abstract

In this paper, we mainly study the solution and properties of the multiterm time‐fractional diffusion equation. First, we obtained the stochastic representation for this equation, which turns to be a subordinated process. Based on the stochastic representation, we calculated the mean square displacement (MSD) and time average mean square displacement, then proved some properties of this model, including subdiffusion, generalized Einstein relationship, and nonergodicity. Finally, a stochastic simulation algorithm was developed for the visualization of sample path of the abnormal diffusion process. The Monte Carlo method was also employed to show the behavior of the solution of this fractional equation.

Suggested Citation

  • Longjin Lv & Luna Wang, 2020. "Stochastic Representation and Monte Carlo Simulation for Multiterm Time‐Fractional Diffusion Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:1315426
    DOI: 10.1155/2020/1315426
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    References listed on IDEAS

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    1. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    2. Grosfils, Patrick & Boon, Jean Pierre, 2006. "Nonextensive statistics in viscous fingering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 168-173.
    3. Metzler, Ralf & Barkai, Eli & Klafter, Joseph, 1999. "Anomalous transport in disordered systems under the influence of external fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 343-350.
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