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On two special classes of fractal surfaces with certain Hausdorff and Box dimensions

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  • Yu, Binyan
  • Liang, Yongshun

Abstract

In this paper, using two special types of rise-dimensional operators based on existing fractal functions, we construct new fractal surfaces with any value of the Hausdorff and Box dimension between two and three. Further, we demonstrate that the lower and upper Box dimension of such fractal surfaces may be unequal to each other. This result could be useful to the research on creating various fractal surfaces with the required fractal dimensions in the future.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006781
    DOI: 10.1016/j.amc.2023.128509
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    References listed on IDEAS

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    1. Verma, Manuj & Priyadarshi, Amit, 2023. "Graphs of continuous functions and fractal dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Ri, SongIl, 2020. "Fractal functions on the Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Binyan Yu & Yongshun Liang, 2022. "Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions," Mathematics, MDPI, vol. 10(13), pages 1-29, June.
    4. Binyan Yu & Yongshun Liang, 2023. "Fractal Dimension Variation Of Continuous Functions Under Certain Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-16.
    5. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Katiyar, S.K. & Chand, A. K. B & Saravana Kumar, G., 2019. "A new class of rational cubic spline fractal interpolation function and its constrained aspects," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 319-335.
    7. 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.
    8. Wu, Junru, 2020. "On a linearity between fractal dimension and order of fractional calculus in Hölder space," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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