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Upper Box Dimension Of Riemann–Liouville Fractional Integral Of Fractal Functions

Author

Listed:
  • Y. S. LIANG

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

  • H. X. WANG

    (College of Arts and Science, New York University, New York 10012, USA)

Abstract

In this paper, we mainly investigate fractal dimension of fractional calculus of certain continuous functions. It has been proved that upper Box dimension of Riemann–Liouville fractional integral of fractal functions whose upper Box dimension is greater than one of certain positive order is at least linearly decreasing. Fractal dimension of Riemann–Liouville fractional integral of any one-dimensional continuous functions with unbounded variation has been proved to be still one-dimensional too. An example about fractal linear interpolation functions shows that estimation is optimal.

Suggested Citation

  • Y. S. Liang & H. X. Wang, 2021. "Upper Box Dimension Of Riemann–Liouville Fractional Integral Of Fractal Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-8, February.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x21500158
    DOI: 10.1142/S0218348X21500158
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