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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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).
    2. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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