Fractional integrals of the Weierstrass functions: The exact box dimension

DOI10.1007/BF02835226zbMath1062.28013OpenAlexW2076692426MaRDI QIDQ4669941

Kui Yao, Wei Yi Su, Song Ping Zhou

Publication date: 15 April 2005

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

Full work available at URL: https://doi.org/10.1007/bf02835226

zbMATH Keywords

Weierstrass functionHausdorff dimensionbox dimensionfractional calculusfractalRiemann-Liouville fractional integral

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 (7)

CARDINALITY AND FRACTAL LINEAR SUBSPACE ABOUT FRACTAL FUNCTIONS ⋮ RELATIONSHIP OF UPPER BOX DIMENSION BETWEEN CONTINUOUS FRACTAL FUNCTIONS AND THEIR RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL ⋮ ON BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL (PARTLY ANSWER FRACTAL CALCULUS CONJECTURE) ⋮ On a class of Besicovitch functions to have exact box dimension: A necessary and sufficient condition ⋮ The fractional derivatives of a fractal function ⋮ THE HADAMARD FRACTIONAL CALCULUS OF A FRACTAL FUNCTION ⋮ The upper bound of box dimension of the Weyl-Marchaud derivative of self-affine curves

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• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
• On multipliers preserving convergence of trigonometric series almost everywhere
• Fractional Brownian Motions, Fractional Noises and Applications

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