Browsing by Author "Xie, He-Ping"

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Chaos synchronization of fractional chaotic maps based on the stability condition
(Elsevier Science Bv, 2016) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Xie, He-Ping; Chen, Fu-Lai
In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann-Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method's effectiveness and fractional chaotic map's potential role for secure communication. (C) 2016 Published by Elsevier B.V.
Discrete Fractional Diffusion Equation of Chaotic Order
(World Scientific Publ Co Pte Ltd, 2016) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; 56389
Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.
Lattice fractional diffusion equation of random order
(Wiley, 2017) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; 56389
The discrete fractional calculus is used to fractionalize difference equations. Simulations of the fractional logistic map unravel that the chaotic solution is conveniently obtained. Then a Riesz fractional difference is defined for fractional partial difference equations on discrete finite domains. A lattice fractional diffusion equation of random order is proposed to depict the complicated random dynamics and an explicit numerical formulae is derived directly from the Riesz difference. Copyright (C) 2015 John Wiley & Sons, Ltd.
Riesz Riemann-Liouville difference on discrete domains
(Aip Publishing, 2016) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Xie, He-Ping
A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically. Published by AIP Publishing.