UPPER BOX DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF FRACTAL FUNCTIONS

Y. S. Liang and H. X. Wang
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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

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-8

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.

Keywords: Riemann–Liouville Fractional Integral; Fractal Dimension; Fractal Function (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x21500158

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DOI: 10.1142/S0218348X21500158

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