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A Note On Fractal Dimension Of Riemann–Liouville Fractional Integral

Author

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  • SUBHASH CHANDRA

    (School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand 175005, Himachal Pradesh India)

  • SYED ABBAS

    (School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand 175005, Himachal Pradesh India)

  • YONGSHUN LIANG

    (Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China)

Abstract

This paper intends to study the analytical properties of the Riemann–Liouville fractional integral and fractal dimensions of its graph on ℠n. We show that the Riemann–Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzelá sense. We also deduce the upper bound of the box dimension and the Hausdorff dimension of the graph of the Riemann–Liouville fractional integral of Hölder continuous functions. Furthermore, we prove that the box dimension and the Hausdorff dimension of the graph of the Riemann–Liouville fractional integral of a function, which is continuous and of bounded variation in Arzelá sense, are n.

Suggested Citation

  • Subhash Chandra & Syed Abbas & Yongshun Liang, 2024. "A Note On Fractal Dimension Of Riemann–Liouville Fractional Integral," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-14.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400012
    DOI: 10.1142/S0218348X24400012
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    Cited by:

    1. Yu, Binyan & Liang, Yongshun, 2024. "On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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