Connection between the order of fractional calculus and fractional dimensions of a type of fractal functions

DOI10.1007/s10496-007-0354-8zbMath1150.41006OpenAlexW2083369939MaRDI QIDQ3513868

Wei Yi Su, Yong Shun Liang

Publication date: 6 August 2008

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

Full work available at URL: https://doi.org/10.1007/s10496-007-0354-8

zbMATH Keywords

fractal dimensionRiemann-Liouville fractional calculusgeneralized Weierstrass function

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25)

Related Items (11)

Fractional derivatives and strain gradient elasticity ⋮ Fractal dimensions of fractional integral of continuous functions ⋮ On a linearity between fractal dimension and order of fractional calculus in Hölder space ⋮ SOME PROPERTIES FOR THE RIEMANN–LIOUVILLE FRACTAL CALCULUS OF CONTINUOUS FUNCTIONS ⋮ On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function ⋮ On \(\Lambda\)-fractional elastic solid mechanics ⋮ HÖLDER CONTINUITY AND BOX DIMENSION FOR THE WEYL FRACTIONAL INTEGRAL ⋮ DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION ⋮ Some remarks on one-dimensional functions and their Riemann-Liouville fractional calculus ⋮ Analytical properties of \((k,s)\)-Riemann-Liouville fractional integral and its fractal dimension ⋮ THE ESTIMATES OF HÖLDER INDEX AND THE BOX DIMENSION FOR THE HADAMARD FRACTIONAL INTEGRAL

Cites Work

• Unnamed Item
• Unnamed Item
• Fractional calculus and its applications. Proceedings of the international conference held at the University of New Haven, June 1974
• On the connection between the order of fractional calculus and the dimensions of a fractal function
• The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus
• The fractal dimensions of graphs of the Weyl-Marchaud fractional derivative of the Weierstrass-type function
• Fractal Dimensions and Singularities of the Weierstrass Type Functions
• THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
• Fractional differentiability of nowhere differentiable functions and dimensions
• Fractional derivatives of Weierstrass-type functions

This page was built for publication: Connection between the order of fractional calculus and fractional dimensions of a type of fractal functions