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Fractals: An Eclectic Survey, Part-I
Fractal and Fractional, 2022 Fractals are geometric shapes and patterns that may repeat their geometry at smaller or larger scales. It is well established that fractals can describe shapes and surfaces that cannot be represented by the classical Euclidean geometry.
Akhlaq Husain +3 more
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Fractals: An Eclectic Survey, Part II
Fractal and Fractional, 2022 Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales.
Akhlaq Husain +3 more
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On the construction of recurrent fractal interpolation functions using Geraghty contractions
Electronic Research Archive, 2023 The recurrent iterated function systems (RIFS) were first introduced by Barnsley and Demko and generalized the usual iterated function systems (IFS). This new method allowed the construction of more general sets, which do not have to exhibit the strict ...
Najmeddine Attia , Hajer Jebali
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The mutual singularity of the relative multifractal measures
Nonautonomous Dynamical Systems, 2021 M. Das proved that the relative multifractal measures are mutually singular for the self-similar measures satisfying the significantly weaker open set condition. The aim of this paper is to show that these measures are mutually singular in a more general
Douzi Zied, Selmi Bilel
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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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Fractals in the Nervous System: Conceptual Implications for Theoretical Neuroscience [PDF]
Front. Physiology, 2009 This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet ...
Gerhard Werner
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Fractal Calculus on Fractal Interpolation Functions [PDF]
Fractal and Fractional, 2021 In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Gowrisankar, Arulprakash +2 more
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Regular, Singular and Hypersingular Integrals over Fractal Contours
Mathematics, 2023 The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals.
Ilya Boykov +2 more
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On the vectorial multifractal analysis in a metric space
AIMS Mathematics, 2023 Multifractal analysis is typically used to describe objects possessing some type of scale invariance. During the last few decades, multifractal analysis has shown results of outstanding significance in theory and applications. In particular, it is widely
Najmeddine Attia, Amal Mahjoub
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