ON THE FRACTIONAL DERIVATIVE OF A TYPE OF SELF-AFFINE CURVES

Kun Yuan Li, Kui Yao and Kai Zhang
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Kun Yuan Li: Department of Foundation Studies, Army Engineering University of PLA, Nanjing 211101, P. R. China
Kui Yao: Department of Foundation Studies, Army Engineering University of PLA, Nanjing 211101, P. R. China
Kai Zhang: College of Command & Control Engineering, Army Engineering, University of PLA, Nanjing 211101, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-7

Abstract: This paper investigates the fractal dimension of the Weyl–Marchaud (W–M) fractional derivative of a type of self-affine curves. We first define the W–M fractional derivative of a general self-affine functions, then calculate the Box dimension of them, finally prove a linear relationship between the order of the W–M fractional derivative and the fractal dimension.

Keywords: Self-affine Function; Weyl–Marchaud Fractional Derivative; Fractal Dimension (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500391

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