IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v462y2016icp1244-1251.html
   My bibliography  Save this article

Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models

Author

Listed:
  • Wei, Song
  • Chen, Wen
  • Hon, Y.C.

Abstract

This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.

Suggested Citation

  • Wei, Song & Chen, Wen & Hon, Y.C., 2016. "Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1244-1251.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1244-1251
    DOI: 10.1016/j.physa.2016.06.145
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116304277
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.06.145?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Baeumer, B. & Benson, D.A. & Meerschaert, M.M., 2005. "Advection and dispersion in time and space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 245-262.
    2. Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J. & Alvarez-Ramirez, Jose, 2007. "Effective medium equations for fractional Fick's law in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 339-353.
    3. Nigmatullin, R.R., 2006. "‘Fractional’ kinetic equations and ‘universal’ decoupling of a memory function in mesoscale region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 282-298.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Palanivel, J. & Suresh, K. & Premraj, D. & Thamilmaran, K., 2018. "Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 35-43.
    2. Fernandez-Anaya, G. & Valdes-Parada, F.J. & Alvarez-Ramirez, J., 2011. "On generalized fractional Cattaneo’s equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4198-4202.
    3. Liwei Shi, 2018. "A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 136-150, August.
    4. Baeumer, B. & Meerschaert, M.M., 2007. "Fractional diffusion with two time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 237-251.
    5. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
    6. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    7. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    8. Kostrobij, P.P. & Markovych, B.M. & Viznovych, O.V. & Tokarchuk, M.V., 2019. "Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 63-70.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1244-1251. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.