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A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function

Author

Listed:
  • Yao, Kui
  • Chen, Haotian
  • Peng, W.L.
  • Wang, Zekun
  • Yao, Jia
  • Wu, Yipeng

Abstract

A new method is applied to calculating fractal dimensions of fractional calculus of some fractal functions, by this method, we obtain Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s096007792030713x
    DOI: 10.1016/j.chaos.2020.110317
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    References listed on IDEAS

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    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. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Yun, CholHui & Ri, MiGyong, 2020. "Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Liang, Yongshun, 2009. "On the fractional calculus of Besicovitch function," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2741-2747.
    5. 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.
    6. 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.
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    Cited by:

    1. Li, Zhiwei & Wang, Jianjian & Yuan, Meng & Wang, Zhongyu & Feng, Pingfa & Feng, Feng, 2022. "An indicator to quantify the complexity of signals and surfaces based on scaling behaviors transcending fractal," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Feng Feng & Meng Yuan & Yousheng Xia & Haoming Xu & Pingfa Feng & Xinghui Li, 2022. "Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    3. Karimui, Reza Yaghoobi, 2021. "A new approach to measure the fractal dimension of a trajectory in the high-dimensional phase space," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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