Browsing by Author "Cheng, De-Fu"

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Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets
(Hindawi LTD, 2013) Zhao, Yang; Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; 56389
The discrete wavelet transform via local fractional operators is structured and applied to process the signals on Cantor sets. An illustrative example of the local fractional discrete wavelet transform is given.
Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators
(Hindawi LTD, 2013) Zhao, Yang; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Cheng, De-Fu; Yang, Xiao-Jun; 56389
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Maxwell's Equations on Cantor Sets: A Local Fractional Approach
(Hindawi LTD, 2013) Zhao, Yang; Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; 56389
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. Local fractional differential forms of Maxwell's equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell's equations for the dynamics of cold dark matter.