IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i5p2538-2545.html
   My bibliography  Save this article

On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function

Author

Listed:
  • Yao, K.
  • Liang, Y.S.
  • Zhang, F.

Abstract

This paper investigates the fractional derivative of a fractal function. It has been proven that there exists certain linear connection between the order of the Weyl-Marchaud fractional derivatives(WMFD) and the Hausdorff dimension of a fractal function. Graphs and numerical results further show this linear relationship.

Suggested Citation

  • Yao, K. & Liang, Y.S. & Zhang, F., 2009. "On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2538-2545.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2538-2545
    DOI: 10.1016/j.chaos.2008.09.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004530
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.09.053?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., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    2. Yao, K. & Liang, Y.S. & Fang, J.X., 2008. "The fractal dimensions of graphs of the Weyl-Marchaud fractional derivative of the Weierstrass-type function," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 106-115.
    3. Liang, Y.S. & Su, W.Y., 2007. "The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 682-692.
    4. El Naschie, M. Saladin, 2006. "Advanced prerequisite for E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 636-641.
    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. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Yao, Kui & Chen, Haotian & Peng, W.L. & Wang, Zekun & Yao, Jia & Wu, Yipeng, 2021. "A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function," Chaos, Solitons & Fractals, Elsevier, vol. 142(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. Yao, K. & Liang, Y.S. & Fang, J.X., 2008. "The fractal dimensions of graphs of the Weyl-Marchaud fractional derivative of the Weierstrass-type function," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 106-115.
    2. Liang, Y.S. & Su, W.Y., 2007. "The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 682-692.
    3. He, Ji-Huan & Wan, Yu-Qin & Xu, Lan, 2007. "Nano-effects, quantum-like properties in electrospun nanofibers," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 26-37.
    4. Yao, Kui & Chen, Haotian & Peng, W.L. & Wang, Zekun & Yao, Jia & Wu, Yipeng, 2021. "A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Nasef, Arafa A. & Hatir, E., 2009. "On fuzzy pre-I-open sets and a decomposition of fuzzy I-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1185-1189.
    6. El Naschie, M.S., 2008. "Fuzzy knot theory interpretation of Yang–Mills instantons and Witten’s 5-Brane model," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1349-1354.
    7. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    8. El Naschie, M.S., 2007. "On the universality class of all universality classes and E-infinity spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 927-936.
    9. El Naschie, M.S., 2009. "Arguments for the compactness and multiple connectivity of our cosmic spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2787-2789.
    10. El Naschie, M.S., 2008. "Quarks confinement," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 6-8.
    11. El Naschie, M.S., 2008. "Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 956-961.
    12. El Naschie, M.S., 2008. "On quarks confinement and asymptotic freedom," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1289-1291.
    13. Nozari, Kourosh & Mehdipour, S. Hamid, 2009. "Failure of standard thermodynamics in planck scale black hole system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 956-970.
    14. 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.
    15. El Naschie, M.S., 2006. "Topics in the mathematical physics of E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 656-663.
    16. El Naschie, M.S., 2008. "The fundamental algebraic equations of the constants of nature," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 320-322.
    17. El Naschie, M.S., 2008. "Quarks confinement via Kaluza–Klein theory as a topological property of quantum classical spacetime phase transition," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 825-829.
    18. Wu, Yahao & Wang, Xiao-Tian & Wu, Min, 2009. "Fractional-moment CAPM with loss aversion," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1406-1414.
    19. Liu, Zhanwei & Hu, Guoen & Lu, Zhibo, 2009. "Parseval frame scaling sets and MSF Parseval frame wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1966-1974.
    20. El Naschie, M.S., 2009. "The crystallographic space groups and Heterotic string theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2282-2284.

    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:41:y:2009:i:5:p:2538-2545. 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.