The Weyl-Marchaud fractional derivative of a type of self-affine functions

DOI10.1016/j.amc.2012.01.077zbMath1250.26008OpenAlexW1965479116MaRDI QIDQ440772

Qi Zhang, Yong Shun Liang

Publication date: 19 August 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.077

zbMATH Keywords

Weierstrass functionbox dimensionBesicovitch functionMarchaud fractional derivativeself-affine functionWeyl

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fractals (28A80)

Related Items (10)

APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION ⋮ Fractal dimensions of fractional integral of continuous functions ⋮ ESTIMATION OF FRACTAL DIMENSION OF FRACTIONAL CALCULUS OF THE HÖLDER CONTINUOUS FUNCTIONS ⋮ Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions ⋮ ON THE BOX DIMENSION OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE AND LINEARITY EFFECT ⋮ A geometric based connection between fractional calculus and fractal functions ⋮ Weyl-Marchaud fractional derivative of a vector valued fractal interpolation function with function contractivity factors ⋮ Analysis of fractal dimension of mixed Riemann-Liouville integral ⋮ WHAT IS THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON THE HÖLDER CONTINUOUS FUNCTIONS? ⋮ FRACTAL DIMENSION ESTIMATION OF THE MARCHAUD FRACTIONAL DIFFERENTIAL OF CERTAIN CONTINUOUS FUNCTIONS

Cites Work

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• The relationship between the box dimension of the Besicovitch functions and the orders of their fractional calculus
• On a class of fractals: the constructive structure
• The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus
• The fractional derivatives of a fractal function
• On a class of Besicovitch functions to have exact box dimension: A necessary and sufficient condition
• The box dimension of self-affine graphs and repellers
• Fractal Dimensions and Singularities of the Weierstrass Type Functions
• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
• Fractional derivatives of Weierstrass-type functions

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