Results 181 to 190 of about 531 (214)
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Fractals, 2022
This study examines the development of a novel approach known as the fractal Elzaki transform method (F[Formula: see text]TM) to investigate the approximation solution of the nonlinear fractal Drinfeld–Sokolov–Wilson (NFDSW) model. We adopt He’s fractal derivative to change the fractal model into its differential parts and then apply the Elzaki ...
FENGLIAN LIU, LEI YANG, MUHAMMAD NADEEM
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This study examines the development of a novel approach known as the fractal Elzaki transform method (F[Formula: see text]TM) to investigate the approximation solution of the nonlinear fractal Drinfeld–Sokolov–Wilson (NFDSW) model. We adopt He’s fractal derivative to change the fractal model into its differential parts and then apply the Elzaki ...
FENGLIAN LIU, LEI YANG, MUHAMMAD NADEEM
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Fractals, 2021
In this paper, the Weyl–Marchaud fractional derivative of various fractal interpolation functions (FIFs) like linear FIF, quadratic FIF, hidden variable FIF and [Formula: see text]-FIF is investigated. Further, the fractal dimension of the quadratic FIF is estimated and it is compared with the order of the Weyl–Marchaud fractional derivative. Besides,
Priyanka, T. M. C., Gowrisankar, A.
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In this paper, the Weyl–Marchaud fractional derivative of various fractal interpolation functions (FIFs) like linear FIF, quadratic FIF, hidden variable FIF and [Formula: see text]-FIF is investigated. Further, the fractal dimension of the quadratic FIF is estimated and it is compared with the order of the Weyl–Marchaud fractional derivative. Besides,
Priyanka, T. M. C., Gowrisankar, A.
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Caputo fractional derivative of $$\alpha $$-fractal spline
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
T. M. C. Priyanka +4 more
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FRACTAL DERIVATIVE MODEL FOR TSUNAMI TRAVELING
Fractals, 2019Tsunami traveling in an unsmooth boundary is studied, where the boundary is considered as a fractal surface, and mass conservation and moment conservation in a fractal space are established, and a fractal derivative-based tsunami model is established. Other discontinuous boundaries can be treated in a similar way.
YAN WANG, QIGEN DENG
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STUDY OF FRACTALS DERIVED FROM IFS-FRACTALS BY METRIC PROCEDURES
Fractals, 2005It is a well-known fact that when visualizing an IFS-attractor through the chaos game, it is possible that the first points mapped will come closer to but stay visibly different from the attractor. This simple fact will be analyzed in more detail, through visualizations of different aspects of this convergence process.
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A New Definition of Fractal Derivative and Stability of Fractal Dynamical Systems
Progress in Fractional Differentiation and ApplicationsIn this paper, we give a novel definition of the fractal derivative and their integral. If r = 1, the definition coincides with the classical definition of the first derivative. Fractal chain rule, fractal exponential functions, fractal Gronwall's inequality, fractal power series expansions, fractal Laplace transforms, and linear fractal differential ...
Sadek, Lakhlifa +2 more
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A Look at Fractal Functions Through Their Fractional Derivatives
Fractals, 1997A relationship between the Lipschitz-Holder exponent and the maximal possible order of derivative is used to look at fractal properties of functions representable by trigonometric series.
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Second Derivative and Curvature of Fractal Curves
2023The theoretical objective of our work is to propose a geometric characterization of surface roughness from fractal models for 3D objects. This characterization will generate groups of geometric models (made up of curves and surfaces) of different kinds of roughness.
Janbein, Mohamad +2 more
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A New Fractal Derivative and its Properties
Progress in Fractional Differentiation and ApplicationsThis study introduces a novel fractal derivative alongside its corresponding integral, delving into essential properties such as the fractal Laplace transform, the fractal chain rule, and derivative operations.We also explore the solution of a linear fractal differential system. Furthermore, we provide two illustrative examples that allow us to compare
Sadek, Lakhlifa +2 more
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The Fractal Dimension of Sets Derived from Complex Bases
Canadian Mathematical Bulletin, 1986AbstractFor each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the ...
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