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Maxwell’s Equations on Cantor Sets: A Local Fractional Approach
Advances in High Energy Physics, 2013 Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields.
Yang Zhao +4 more
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Data block decomposition and intelligent secure acquisition of microdata
Scientific Reports, 2023 P-sets (P stands for Packet) is a set model with dynamic characteristics, which is obtained by introducing dynamic characteristics into Cantor set and improving Cantor set. According to the fact that the characteristics of class I big data are completely
Xiuquan Zhang, Lin Shen, Kaiquan Shi
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Advances in Mathematical Physics, 2013 The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators.
Ya-Juan Hao +3 more
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Exhaustible sets in higher-type computation [PDF]
Logical Methods in Computer Science, 2008 We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which the predicate ...
Martin Escardo
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Analysis of the n-Term Klein-Gordon Equations in Cantor Sets
Chaos Theory and Applications, 2023 The effectiveness of the local fractional reduced differential transformation method (LFRDTM) for the approximation of the solution related to the extended n-term local fractional Klein-Gordon equation is the main aim of this paper in which fractional ...
Nikhil Sharma +2 more
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Journal of Approximation Theory, 2014 We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in Stahl-Totik sense.
Gökalp Alpan, Alexander Goncharov
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Abstract and Applied Analysis, 2014 We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed.
Ai-Min Yang +6 more
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Fractal and Fractional, 2023 A new local fractional modified Benjamin–Bona–Mahony equation is proposed within the local fractional derivative in this study for the first time. By defining some elementary functions via the Mittag–Leffler function (MLF) on the Cantor sets (CSs), a set
Kang-Jia Wang, Feng Shi
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Characterization of the Local Growth of Two Cantor-Type Functions
Fractal and Fractional, 2019 The Cantor set and its homonymous function have been frequently utilized as examples for various physical phenomena occurring on discontinuous sets.
Dimiter Prodanov
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On the Exact Solution of Wave Equations on Cantor Sets
Entropy, 2015 The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of ...
Dumitru Baleanu +3 more
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