On a class of fractals: the constructive structure

DOI10.1016/S0960-0779(03)00282-0zbMath1068.28009OpenAlexW2061970362MaRDI QIDQ1877951

G. L. He, Tingfan Xie, Song Ping Zhou

Publication date: 19 August 2004

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(03)00282-0

zbMATH Keywords

box dimensionfractalsBesicovitch function

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fractals (28A80) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Lacunary series of trigonometric and other functions; Riesz products (42A55) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items

THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL ⋮ On the fractional calculus of Besicovitch function ⋮ FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION ⋮ The relationship between the order of \((k, s)\)-Riemann-Liouville fractional integral and the fractal dimensions of a fractal function ⋮ The Weyl-Marchaud fractional derivative of a type of self-affine functions ⋮ The relationship between the box dimension of the Besicovitch functions and the orders of their fractional calculus ⋮ On a class of fractal functions with graph Hausdorff dimension 2 ⋮ The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus ⋮ On the connection between the order of fractional calculus and the dimensions of a fractal function ⋮ THE HADAMARD FRACTIONAL CALCULUS OF A FRACTAL FUNCTION

Cites Work

• Unnamed Item
• Unnamed Item
• On dimensions of Cantor set related systems
• The Minkowski dimension and critical effects in fractal evolution of defects
• On a class of Besicovitch functions to have exact box dimension: A necessary and sufficient condition
• On the Weierstrass-Mandelbrot fractal function
• Fractal Dimensions and Singularities of the Weierstrass Type Functions
• Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous Curves