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On the fractional calculus of Besicovitch function

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  • Liang, Yongshun

Abstract

Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann–Liouville fractional calculus and Weyl–Marchaud fractional derivative of Besicovitch function have been discussed.

Suggested Citation

  • Liang, Yongshun, 2009. "On the fractional calculus of Besicovitch function," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2741-2747.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2741-2747
    DOI: 10.1016/j.chaos.2009.03.180
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    References listed on IDEAS

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    1. 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. 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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