The fractional derivatives of a fractal function

DOI10.1007/s10114-005-0644-zzbMath1106.28004OpenAlexW1985069571MaRDI QIDQ2508593

Kui Yao, Song Ping Zhou, Wei Yi Su

Publication date: 13 October 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0644-z

zbMATH Keywords

Weierstrass functiongraph dimensions

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Fractional derivatives and integrals (26A33) Fractals (28A80)

Related Items (14)

A new method on box dimension of Weyl-Marchaud fractional derivative of Weierstrass function ⋮ APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION ⋮ Letnikov vs. Marchaud: a survey on two prominent constructions of fractional derivatives ⋮ Fractal dimensions of fractional integral of continuous functions ⋮ On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function ⋮ Fractional square functions and potential spaces. II ⋮ CONSTRUCTION OF NEW AFFINE AND NON-AFFINE FRACTAL INTERPOLATION FUNCTIONS THROUGH THE WEYL–MARCHAUD DERIVATIVE ⋮ Boundedness and convergence on fractional order systems ⋮ FRACTIONAL EULER-LAGRANGE AND FRACTIONAL HAMILTON EQUATIONS FOR SUPER SYMMETRIC CLASSICAL MODEL ⋮ DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION ⋮ The Weyl-Marchaud fractional derivative of a type of self-affine functions ⋮ A generalization of the concept of \(q\)-fractional integrals ⋮ Fractional calculus for multivariate vector-valued function and fractal function ⋮ ANALYSIS ON WEYL–MARCHAUD FRACTIONAL DERIVATIVE FOR TYPES OF FRACTAL INTERPOLATION FUNCTION WITH FRACTAL DIMENSION

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• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
• Fractional differentiability of nowhere differentiable functions and dimensions
• Fractional integrals of the Weierstrass functions: The exact box dimension
• Fractional derivatives of Weierstrass-type functions

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