ON THE BOX DIMENSION OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE AND LINEARITY EFFECT

Subhash Chandra (), Syed Abbas and Yongshun Liang ()
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Subhash Chandra: School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175005, India
Syed Abbas: School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175005, India
Yongshun Liang: ��School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-8

Abstract: This paper intends to estimate the box dimension of the Weyl–Marchaud fractional derivative (Weyl–M derivative) for various choices of continuous functions on a compact subset of ℠. We show that the Weyl–M derivative of order γ of a continuous function satisfying Hölder condition of order μ also satisfies Hölder condition of order μ − γ and the upper box dimension of the Weyl–M derivative increases at most linearly with the order γ. Moreover, the upper box dimension of the Weyl–M derivative of a continuous function satisfying the Lipschitz condition is not more than the sum of the box dimension of the function itself and order γ. Furthermore, we prove that the box dimension of the Weyl–M derivative of a certain continuous function which is of bounded variation is one.

Keywords: Box Dimension; Weyl–Marchaud Fractional Derivative; Hölder Condition; Bounded Variation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500585

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