WHAT IS THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON THE HÖLDER CONTINUOUS FUNCTIONS?

X. X. Cui and W. Xiao
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X. X. Cui: Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
W. Xiao: Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-7

Abstract: Let f(t) be α-Hölder continuous on ℠and well-defined about the Weyl fractional integral. Then, dim¯BΓ(f, [0, 1]) ≤ 2 − αanddim¯BΓ(Wνf, [0, 1]) ≤ 2 − α − ν, where Wνf(x) = 1 Γ(ν)∫x∞(t − x)ν−1f(t)dt and 0 < α,α + ν < 1. This estimation shows that the Box dimension of Wνf(x) leads to some similar linear dimension decrease like the Riemann–Liouville fractional integral [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of continuous functions, Acta Math. Sin. 32 (2016) 1494–1508].

Keywords: The Box Dimension; The Weyl Fractional Integral; α-Hölder Continuous (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500262

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