IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i4p923-929.html
   My bibliography  Save this article

Time–space fabric underlying anomalous diffusion

Author

Listed:
  • Chen, W.

Abstract

This study unveils the time–space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time–space fabric on physical behaviors and accordingly derive fractional quantum relationships between energy and frequency, momentum and wavenumber which further give rise to fractional Schrödinger equation. As an alternative modeling approach to the standard fractional derivatives, we introduce the concept of the Hausdorff derivative underlying the Hausdorff dimensions of metric spacetime. And in terms of the proposed hypotheses, the Hausdorff derivative is used to derive a linear anomalous transport–diffusion equation underlying anomalous diffusion process. Its Green’s function solution turn out to be a stretched Gaussian distribution and is compared with that from the Richardson’s turbulence diffusion equation.

Suggested Citation

  • Chen, W., 2006. "Time–space fabric underlying anomalous diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 923-929.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:923-929
    DOI: 10.1016/j.chaos.2005.08.199
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905008544
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.08.199?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. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    2. A. La Porta & Greg A. Voth & Alice M. Crawford & Jim Alexander & Eberhard Bodenschatz, 2001. "Fluid particle accelerations in fully developed turbulence," Nature, Nature, vol. 409(6823), pages 1017-1019, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    3. Shojaeizadeh, T. & Mahmoudi, M. & Darehmiraki, M., 2021. "Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Imran, M.A., 2020. "Application of fractal fractional derivative of power law kernel (FFP0Dxα,β) to MHD viscous fluid flow between two plates," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Balankin, Alexander S., 2020. "Fractional space approach to studies of physical phenomena on fractals and in confined low-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
    7. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    8. ARAZ, Seda İĞRET, 2020. "Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Tian, Peibo & Liang, Yingjie, 2022. "Material coordinate driven variable-order fractal derivative model of water anomalous adsorption in swelling soil," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

    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. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    2. ElOkaby, Ayman A., 2007. "A short review of the Higgs boson mass and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 14-25.
    3. Huang, Yongdong & Cheng, Zhengxing, 2007. "Minimum-energy frames associated with refinable function of arbitrary integer dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 503-515.
    4. Sergeyev, Yaroslav D., 2009. "Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3042-3046.
    5. Chen, Qingjiang & Cheng, Zhengxing, 2007. "A study on compactly supported orthogonal vector-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1024-1034.
    6. Qiu, Hua & Su, Weiyi, 2007. "3-Adic Cantor function on local fields and its p-adic derivative," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1625-1634.
    7. Mesón, Alejandro & Vericat, Fernando, 2009. "Simultaneous multifractal decompositions for the spectra of local entropies and ergodic averages," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2353-2363.
    8. He, Ji-Huan, 2006. "Application of E-infinity theory to biology," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 285-289.
    9. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.
    10. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    11. Na, Ji Sung & Koo, Eunmo & Ko, Seung Chul & Linn, Rodman & Muñoz-Esparza, Domingo & Jin, Emilia Kyung & Lee, Joon Sang, 2019. "Stochastic characteristics for the vortical structure of a 5-MW wind turbine wake," Renewable Energy, Elsevier, vol. 133(C), pages 1220-1230.
    12. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    13. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    14. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    15. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
    16. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    17. El Naschie, M.S., 2006. "E-infinity theory—Some recent results and new interpretations," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 845-853.
    18. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    19. El Naschie, Mohamed Saladin, 2006. "Is gravity less fundamental than elementary particles theory? Critical remarks on holography and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 803-807.
    20. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.

    More about this item

    Statistics

    Access and download statistics

    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:chsofr:v:28:y:2006:i:4:p:923-929. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.