FRACTAL DIMENSION ESTIMATION OF THE MARCHAUD FRACTIONAL DIFFERENTIAL OF CERTAIN CONTINUOUS FUNCTIONS

Yong-Shun Liang and Qi Zhang ()
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Yong-Shun Liang: School of Science, Nanjing University of Science and Technology, Campus Mailbox No. 200 Xiaolingwei, Qinhuai District, Nanjing 210094, P. R. China
Qi Zhang: Faculty of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-6

Abstract: In this paper, we mainly investigate the fractional differential of a class of continuous functions. The upper Box dimension of the Marchaud fractional differential of continuous functions satisfying the Hölder condition increases at most linearly with the order of the fractional differential when they exist. Furthermore, if a continuous function satisfies the Lipschitz condition, the upper Box dimension of its Marchaud fractional differential is at most the sum of one and order of the fractional differential when it exists. From the point of view of the fractal dimension, it increases at most linearly with the fractional order.

Keywords: The Fractal Dimension; The Lipschitz Condition; The Hölder Condition; The Marchaud Fractional Differential; Unbounded Variation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501711

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