On a class of Besicovitch functions to have exact box dimension: A necessary and sufficient condition

DOI10.1007/BF02901441zbMath1058.28007OpenAlexW2072258008MaRDI QIDQ4662069

G. L. He, Song Ping Zhou

Publication date: 30 March 2005

Published in: Analysis in Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02901441

zbMATH Keywords

Weierstrass functionbox dimensionfractal dimensionfractional integral operatorBesicovitch functionfractional Riemann-Liouville differential operatorHardamard condition

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fractals (28A80) Hausdorff and packing measures (28A78) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (1)

Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus

Cites Work

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• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
• Fractional integrals of the Weierstrass functions: The exact box dimension
• Fractional Brownian Motions, Fractional Noises and Applications
• Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous Curves

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