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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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Stable intersections of conformal Cantor sets [PDF]
Ergodic Theory and Dynamical Systems, 2021 AbstractWe investigate stable intersections of conformal Cantor sets and their consequences to dynamical systems. First we define this type of Cantor set and relate it to horseshoes appearing in automorphisms of $\mathbb {C}^2$ . Then we study limit geometries, that is, objects related to the asymptotic shape of the Cantor sets, to obtain a criterion ...
Araújo, Hugo, Moreira, Carlos Gustavo
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Cuntz–Krieger Algebras and Wavelets on Fractals [PDF]
, 2011 We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval.
Marcolli, Matilde, Paolucci, Anna Maria
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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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Weakly Equilibrium Cantor-type Sets [PDF]
Potential Analysis, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Topology and its Applications, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gutev, V. +3 more
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