On a class of fractals: the constructive structure

Zhou, S. P.; He, Guanghua; Xie, Tingfan

doi:10.1016/s0960-0779(03)00282-0

Cited by 15 publications

(4 citation statements)

References 7 publications

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“…Let us take x = y = ξ, ν = iτ then after simplifying we get During the last three decade, many mathematical methods were widely applied in fractal analysis. Fractional calculus used to investigate fractal functions is an important tool in this fields [13]. The main physical purpose for investigating fractional diffusion equations is to describe phenomena of anomalous diffusion.…”

Section: Solutionmentioning

confidence: 99%

Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms

Aghili

2021

J. Numer. Anal. Approx. Theory

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Section: Solutionmentioning

confidence: 99%

Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms

Aghili

2021

J. Numer. Anal. Approx. Theory

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“…[8][9][10][11] Fractional calculus such as RiemannLiouville fractional calculus 4,12 which has been used to investigate fractal curves is an important tool in the fractal analysis. Liang 12 carried out research on Riemann-Liouville fractional integral of continuous functions with bounded variation.…”

Section: Introductionmentioning

confidence: 99%

Fractal Dimension of Riemann–liouville Fractional Integral of Certain Unbounded Variational Continuous Function

Xiao

2017

Fractals

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“…The power spectral density function for the error surface described by W-M fractal function can be obtained by discrete Fourier transformation (Zhou and He, 2004):…”

Section: Introductions the Sample And Experiments Conditionmentioning

confidence: 99%

Reconstruction of surface errors of the metallic waveguide based on electromagnetic scattering theory

Tang

2016

IJSURFSE

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Abstract:First, the fractal model of surface errors was constructed by means of the Monte Carlo method, and the source term and spectral amplitude of surface errors were calculated. The reconstruction model of surface errors was then established. The non-differentiable problem of the fractal model was solved by the fractional differential theory. To verify the accuracy of proposed models, a waveguide filter was manufactured. The reconstruction results obtained by the fractal function model were compared with the measured results, and a comparison of the results obtained by different reconstruction models proves that the fractal function is optimal in modelling.Keywords: reconstruction; surface error; metallic waveguide; electromagnetic scattering; fractal function.Reference to this paper should be made as follows: Li, N. and Tang, B. (2016) 'Reconstruction of surface errors of the metallic waveguide based on electromagnetic scattering theory', Int.

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On a class of fractals: the constructive structure

Cited by 15 publications

References 7 publications

Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms

Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms

Fractal Dimension of Riemann–liouville Fractional Integral of Certain Unbounded Variational Continuous Function

Reconstruction of surface errors of the metallic waveguide based on electromagnetic scattering theory

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