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

KUN YUAN LI

Department of Foundation Studies, Army Engineering University of PLA, Nanjing 211101, P. R. China

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KUI YAO

https://orcid.org/0000-0002-1227-336X

Department of Foundation Studies, Army Engineering University of PLA, Nanjing 211101, P. R. China

E-mail Address: yaokuinju@tom.com

Corresponding author.

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, and

KAI ZHANG

College of Command & Control Engineering, Army Engineering, University of PLA, Nanjing 211101, P. R. China

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https://doi.org/10.1142/S0218348X23500391Cited by:0 (Source: Crossref)

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:

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