On a linearity between fractal dimension and order of fractional calculus in Hölder space

DOI10.1016/j.amc.2020.125433zbMath1474.26012OpenAlexW3036740550MaRDI QIDQ2657306

Junru Wu

Publication date: 12 March 2021

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

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125433

zbMATH Keywords

box dimensionfractal dimensionRiemann-Liouville fractional integralHölder condition

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Fractional derivatives and integrals (26A33)

Related Items (11)

APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION ⋮ A brief note on fractal dynamics of fractional Mandelbrot sets ⋮ ON RIEMANN–LIOUVILLE FRACTIONAL DIFFERENTIABILITY OF CONTINUOUS FUNCTIONS AND ITS PHYSICAL INTERPOLATION ⋮ R-L ALGORITHM: AN APPROXIMATION ALGORITHM FOR FRACTAL SIGNALS BASED ON FRACTIONAL CALCULUS ⋮ Active control and electronic simulation of a novel fractional order chaotic jerk system ⋮ A geometric based connection between fractional calculus and fractal functions ⋮ On initial value problems of fractal delay equations ⋮ Analysis of fractal dimension of mixed Riemann-Liouville integral ⋮ Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions ⋮ UPPER BOX DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF FRACTAL FUNCTIONS ⋮ ANALYSIS OF MIXED WEYL–MARCHAUD FRACTIONAL DERIVATIVE AND BOX DIMENSIONS

Cites Work

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• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
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• THE EFFECTS OF THE RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL ON THE BOX DIMENSION OF FRACTAL GRAPHS OF HÖLDER CONTINUOUS FUNCTIONS
• Fractional derivatives of Weierstrass-type functions

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