Results 201 to 210 of about 5,343,237 (227)

A TYPE OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR FRACTIONAL CALCULUS

Fractals, 2016
Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann–Liouville fractional calculus and Box dimension of FIF has been ...
Liang, Yong-Shun, Zhang, Qi
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Hidden Variable Fractal Interpolation Functions

SIAM Journal on Mathematical Analysis, 1989
Interpolation functions $f:[0,1] \to \mathbb{R}$ of the following nature are constructed. Given data \[ \left\{ {\left( {t_n ,x_n } \right) \in [0,1] \times \mathbb{R}:n = 0,1,2, \cdots ,N} \right\}\] with $0 = t_0 < t_1 < \cdots
M. F. Barnsley, J. Elton, D. Hardin, P. Massopust   +3 more
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Fractal Interpolation Function for Countable Data

2020
The problem of extending the theory of an iterated function system carried over to an infinite and countable iterated function system has been widely studied in the last decades. Such an extension is applied in the theory of sampling and reconstruction where a countable iterated function system contributes to a better approximation.
Santo Banerjee, D. Easwaramoorthy, A. Gowrisankar   +2 more
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Node insertion in Coalescence Fractal Interpolation Function

Chaos, Solitons & Fractals, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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THE NON-DIFFERENTIABILITY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS

Acta Mathematica Scientia, 1999
Summary: \textit{D. P. Hardin} and \textit{P. R. Massopust} [Commun. Math. Phys. 105, 455-460 (1986; Zbl 0605.28006)] introduced a class of fractal interpolation functions and calculated their Bouligand dimensions. This paper deals with the non-differentiability of these functions and shows some conditions under which they are nowhere differentiable.
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A class of functional equation and fractal interpolation functions

Applied Mathematics-A Journal of Chinese Universities, 1999
The author considers the functional equation \[ L(\psi_{\omega})=\sum_{j=1}^{\infty} a_j L(\psi_{\sigma^j \omega})+f(\psi_{\omega}), \tag{E} \] where \(f \in C([0,1])\), \(f(0)=f(1)=0\), is a given function, \(\omega=(i_1,i_2,\cdots,i_k,\cdots)\), \(i_k\in(0,1,\cdots,N-1)\), \(\sigma^j\omega=(i_{j+1},\cdots)\), \(\psi_{\omega}=\sum_{k=1}^{\infty} \frac{
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Multifractal analysis of fractal interpolation functions

Physica Scripta
Abstract This paper presents a novel algorithm to utilize multifractal spectrum as a quantitative measure for the fractal interpolation functions with respect to scaling factor and fractional order. As of yet, there were no error estimation techniques to interpret the fractal interpolation functions in the literature. To bridge this gap,
T M C Priyanka, A Gowrisankar
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Zipper rational fractal interpolation functions

The Journal of Analysis
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Pasupathi, null Vijay, A. K. B. Chand, N. S. Upadhye   +3 more
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Construction and box dimension of the composite fractal interpolation function

Chaos, Solitons and Fractals, 2023
Zhong Dai, Shutang Liu
exaly  

On the Variable Order Fractional Calculus Characterization for the Hidden Variable Fractal Interpolation Function

Fractal and Fractional, 2023
A Gowrisankar
exaly