Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 22Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets(Hindawi Ltd, 2013) Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; Zhao, YangThe 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.Article Citation - WoS: 53Citation - Scopus: 65Maxwell's Equations on Cantor Sets: a Local Fractional Approach(Hindawi Ltd, 2013) Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; Zhao, YangMaxwell'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.Article Citation - WoS: 20Citation - Scopus: 20Local Fractional Poisson and Laplace Equations With Applications To Electrostatics in Fractal Domain(Hindawi Ltd, 2014) Zhao, Yang; Xie, Gong-Nan; Baleanu, Dumitru; Yang, Xiao-Jun; Zhao, Kai; Li, Yang-YangFrom the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. Their applications to the electrostatics in fractal media are discussed and their local forms in the Cantor-type cylindrical coordinates are also obtained.Article Citation - WoS: 2Citation - Scopus: 2On the Nonlinear Perturbation K(N, M) Rosenau-Hyman Equation: a Model of Nonlinear Scattering Wave(Hindawi Ltd, 2015) Baleanu, Dumitru; Al Qurashi, Maysaa' Mohamed; Yang, Xiao-Jun; Atangana, AbdonWe investigate a nonlinear wave phenomenon described by the perturbation K(m, n) Rosenau-Hyman equation within the concept of derivative with fractional order. We used the Caputo fractional derivative and we proposed an iteration method in order to find a particular solution of the extended perturbation equation. We proved the stability and the convergence of the suggested method for solving the extended equation without any restriction on (m, n) and also on the perturbations terms. Using the inner product we proved the uniqueness of the special solution. By choosing randomly the fractional orders and m, we presented the numerical solutions.Article Citation - WoS: 5Citation - Scopus: 14Mappings for Special Functions on Cantor Sets and Special Integral Transforms Via Local Fractional Operators(Hindawi Ltd, 2013) Baleanu, Dumitru; Baleanu, Mihaela Cristina; Cheng, De-Fu; Yang, Xiao-Jun; Zhao, YangThe 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.Article Citation - WoS: 43Citation - Scopus: 80Local Fractional Sumudu Transform With Application To Ivps on Cantor Sets(Hindawi Ltd, 2014) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, H. M.Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the non differentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.Article Citation - WoS: 26Citation - Scopus: 22On Local Fractional Continuous Wavelet Transform(Hindawi Ltd, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunWe introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.Article Citation - WoS: 16Citation - Scopus: 27Fractal Dynamical Model of Vehicular Traffic Flow Within the Local Fractional Conservation Laws(Hindawi Ltd, 2014) Yang, Xiao-Jun; Baleanu, Dumitru; Cattani, Carlo; Zhao, Yang; Wang, Long-FeiWe suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.Article Citation - WoS: 48Citation - Scopus: 53One-Phase Problems for Discontinuous Heat Transfer in Fractal Media(Hindawi Ltd, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Hu, Ming-ShengWe first propose the fractal models for the one-phase problems of discontinuous transient heat transfer. The models are taken in sense of local fractional differential operator and used to describe the (dimensionless) melting of fractal solid semi-infinite materials initially at their melt temperatures.Article Citation - WoS: 30Citation - Scopus: 60A Local Fractional Variational Iteration Method for Laplace Equation Within Local Fractional Operators(Hindawi Ltd, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Yang, Yong-JuThe local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.