A note on Katugampola fractional calculus and fractal dimensions
From MaRDI portal
Publication:2007517
DOI10.1016/j.amc.2018.07.035zbMath1428.28018OpenAlexW2887637822MaRDI QIDQ2007517
Publication date: 22 November 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2018.07.035
bounded variationHausdorff dimensionbox dimensionKatugampola fractional calculusunbounded variation point
Fractional derivatives and integrals (26A33) Fractals (28A80) Hausdorff and packing measures (28A78) Functions of bounded variation, generalizations (26A45)
Related Items (16)
Fractal dimension of graph of Katugampola fractional integral and some general characterizations ⋮ Construction of new fractal interpolation functions through integration method ⋮ The fractional space-time radial diffusion equation in terms of the Fox's \(H\)-function ⋮ Bases consisting of self-referential functions in Banach spaces ⋮ ESTIMATION OF FRACTAL DIMENSION OF FRACTIONAL CALCULUS OF THE HÖLDER CONTINUOUS FUNCTIONS ⋮ Dimensional analysis of mixed Riemann-Liouville fractional integral of vector-valued functions ⋮ FRACTAL DIMENSIONS OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE OF CERTAIN ONE-DIMENSIONAL FUNCTIONS ⋮ A geometric based connection between fractional calculus and fractal functions ⋮ ESTIMATION OF FRACTAL DIMENSION OF WEYL FRACTIONAL INTEGRAL OF CERTAIN CONTINUOUS FUNCTIONS ⋮ COMPOSITION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS AND THEIR RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL ⋮ Katugampola fractional integral and fractal dimension of bivariate functions ⋮ Fractional calculus for multivariate vector-valued function and fractal function ⋮ UPPER BOX DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF FRACTAL FUNCTIONS ⋮ ANALYSIS OF MIXED WEYL–MARCHAUD FRACTIONAL DERIVATIVE AND BOX DIMENSIONS ⋮ FURTHER DISCUSSION ABOUT FRACTIONAL DIFFERENTIABILITY OF CERTAIN CONTINUOUS FUNCTIONS ⋮ RELATIONSHIP BETWEEN UPPER BOX DIMENSION OF CONTINUOUS FUNCTIONS AND ORDERS OF WEYL FRACTIONAL INTEGRAL
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- New approach to a generalized fractional integral
- Box dimensions of Riemann-Liouville fractional integrals of continuous functions of bounded variation
- Fractional calculus and its applications. Proceedings of the international conference held at the University of New Haven, June 1974
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Fractional integral and its physical interpretation
- Generalized fractional integral inequalities for continuous random variables
- Variational problems involving a Caputo-type fractional derivative
- Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations
- Fractional differential equations of Caputo-Katugampola type and numerical solutions
- Some remarks on one-dimensional functions and their Riemann-Liouville fractional calculus
- The Hausdorff dimension of graphs of Weierstrass functions
- FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION
- DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION
- A New Approach to Generalized Fractional Derivatives
- Properties of the Katugampola fractional derivative with potential application in quantum mechanics
- DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION
- FRACTAL DIMENSION OF CERTAIN CONTINUOUS FUNCTIONS OF UNBOUNDED VARIATION
- BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL OF CONTINUOUS FUNCTIONS OF BOUNDED AND UNBOUNDED VARIATION
- An approximation formula for the Katugampola integral
- Extreme values of some continuous nowhere differentiable functions
- Physical and geometrical interpretation of fractional operators
This page was built for publication: A note on Katugampola fractional calculus and fractal dimensions
