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What Is The Effect Of The Weyl Fractional Integral On The Hã–Lder Continuous Functions?

Author

Listed:
  • X. X. CUI

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

  • W. XIAO

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

Abstract

Let f(t) be α-Hölder continuous on ℠and well-defined about the Weyl fractional integral. Then, dim¯BΓ(f, [0, 1]) ≤ 2 − αanddim¯BΓ(Wνf, [0, 1]) ≤ 2 − α − ν, where Wνf(x) = 1 Γ(ν)∫x∞(t − x)ν−1f(t)dt and 0 < α,α + ν < 1. This estimation shows that the Box dimension of Wνf(x) leads to some similar linear dimension decrease like the Riemann–Liouville fractional integral [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, Acta Math. Sin. 32 (2016) 1494–1508].

Suggested Citation

  • X. X. Cui & W. Xiao, 2021. "What Is The Effect Of The Weyl Fractional Integral On The Hã–Lder Continuous Functions?," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-7, February.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x21500262
    DOI: 10.1142/S0218348X21500262
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    Cited by:

    1. Yu, Binyan & Liang, Yongshun, 2024. "On two special classes of fractal surfaces with certain Hausdorff and Box dimensions," Applied Mathematics and Computation, Elsevier, vol. 468(C).

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