New relationships connecting a class of fractal objects and fractional integrals in space

DOI10.2478/s13540-013-0056-1zbMath1312.28008OpenAlexW1969683226MaRDI QIDQ2347381

Dumitru Baleanu, Raoul R. Nigmatullin

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-013-0056-1

zbMATH Keywords

Cantor setaveraging of smooth functions on spatial fractal setsfractal objectself-similar objectspatial fractional integralCantor set: fractal object

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Fractional derivatives and integrals (26A33) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Self-similar stochastic processes (60G18) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items

Fractional calculus: D'où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016) ⋮ Double Laplace Transform and Explicit Fractional Analogue of 2D Laplacian ⋮ ON RIEMANN–LIOUVILLE FRACTIONAL DIFFERENTIABILITY OF CONTINUOUS FUNCTIONS AND ITS PHYSICAL INTERPOLATION ⋮ Some pioneers of the applications of fractional calculus ⋮ Accurate relationships between fractals and fractional integrals: new approaches and evaluations ⋮ PROGRESS ON ESTIMATION OF FRACTAL DIMENSIONS OF FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS ⋮ Complex-order fractional diffusion in reaction-diffusion systems ⋮ A geometric based connection between fractional calculus and fractal functions ⋮ Fractional calculus involving \((p, q)\)-Mathieu type series ⋮ Sub- and super-diffusion on Cantor sets: beyond the paradox ⋮ ``Fuzzy calculus: the link between quantum mechanics and discrete fractional operators ⋮ Spontaneous activation under atrial fibrosis: a model using complex order derivatives ⋮ RELATIONSHIP BETWEEN UPPER BOX DIMENSION OF CONTINUOUS FUNCTIONS AND ORDERS OF WEYL FRACTIONAL INTEGRAL

Cites Work

• Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
• Universal distribution function for the strongly-correlated fluctuations: general way for description of different random sequences
• Recent history of fractional calculus
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The derivation of the generalized functional equations describing self-similar processes
• Microscopic model of dielectric \(\alpha\)-relaxation in disordered media
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: New relationships connecting a class of fractal objects and fractional integrals in space