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The fractal dimensions of graphs of the Weyl-Marchaud fractional derivative of the Weierstrass-type function

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  • Yao, K.
  • Liang, Y.S.
  • Fang, J.X.

Abstract

The fractal dimensions of graphs of the Weyl-Marchaud fractional derivative of the Weierstrass-type function have been calculated. And the linear relationship between the fractal dimensions of graphs of the Weierstrass-type function and the orders of their Weyl-Marchaud fractional derivative has been get. Graphs and numerical results of certain examples have further certificated this interesting relationship.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:1:p:106-115
    DOI: 10.1016/j.chaos.2007.04.017
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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. 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. 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, 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.
    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).

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