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Fractal Dimension for a Class of Complex-Valued Fractal Interpolation Functions
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of our paper...
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Fractal Dimension of Random Attractor for a Stochastic Lattice System with White Noise
In this paper, it was studied the finite fractal dimension of random attractor for the stochastic Klein-Gordon-Schrödinger (KGS) lattice equation...
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Fractal dimension of random invariant sets and regular random attractors for stochastic hydrodynamical equations
The main aim of this work is to provide some general and unified results on the existence, regularity and finite fractal dimension estimates of...
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On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures
In this article, our aim is to estimate the fractal dimensions of the graphs of fractal interpolation functions (FIFs) on the product of two...
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Fractal Laplace transform: analyzing fractal curves
The concept of Laplace transform has been extended to fractal curves, enabling the solution of fractal differential equations with constant...
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A Geometric Based Connection between Fractional Calculus and Fractal Functions
Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory. In...
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Fractal Paradigm
This opening essay provides the medical practitioner, biophysical researcher, and student (of any age) with an introduction to a new vocabulary based...
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On the Localization of Fractal Lines of Discontinuity from Noisy Data
AbstractAn ill-posed problem of localization (determining the position) of discontinuity lines of a function of two variables is considered: outside...
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Characterization of synthetic porous media images by using fractal and multifractal analysis
Fractal and multifractal analysis of porous images allow the description of porous media through a scale-invariant understanding. There have been...
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Box Dimension and Fractional Integrals of Multivariate \(\alpha \)-Fractal Functions
In this article, we construct multivariate fractal interpolation functions for a given set of data points and explore the existence of the
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Fractal Calculus for CERTs
Operator algebra is introduced without being explicit about how we do things but hopefully conveys in words what we do not show with formal...
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Existence, stability, and numerical simulations of a fractal-fractional hepatitis B virus model
This paper uses a new fractal-fractional operator with a power law-type kernel in the Riemann-Liouville sense to formulate the new fractal-fractional...
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Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus
In this paper, we mainly make research on the approximation of continuous functions in the view of the fractal structure based on previous studies....
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A new type of zipper fractal interpolation surfaces and associated bivariate zipper fractal operator
This note aims to introduce a bivariate fractal interpolation method by using the concept of zipper. In this note, we establish a general method to...
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The relationship between the order of (k, s)-Riemann-Liouville fractional integral and the fractal dimensions of a fractal function
This paper mainly investigates the relationship between the fractal dimension of the graph of the ( k , s )-Riemann-Liouville fractional integral and...
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Katugampola Fractional Integral and Fractal Dimension of Bivariate Functions
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane....
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Dimension preserving approximation
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on [0, 1] and initiates the study of...
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Fractal surfaces in Hölder and Sobolev spaces
Following the construction of fractal surfaces due to Ruan and Xu (Bulletin of the Australian Mathematical Society 91:435–446, 2015) and the theory...
