Browsing by Author "Deng, Zhen-Guo"

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Discrete fractional diffusion equation
(Springer, 2015) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Zeng, Sheng-Da; Deng, Zhen-Guo
The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta's sense. The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.
Lattice fractional diffusion equation in terms of a Riesz-Caputo difference
(Elsevier, 2015) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Deng, Zhen-Guo; Zeng, Sheng-Da
A fractional difference is defined by the use of the right and the left Caputo fractional differences. The definition is a two-sided operator of Riesz type and introduces back and forward memory effects in space difference. Then, a fractional difference equation method is suggested for anomalous diffusion in discrete finite domains. A lattice fractional diffusion equation is proposed and the numerical simulation of the diffusion process is discussed for various difference orders. The result shows that the Riesz difference model is particularly suitable for modeling complicated dynamical behaviors on discrete media. (C) 2015 Elsevier B.V. All rights reserved.
New variable-order fractional chaotic systems for fast image encryption
(Amer inst Physics, 2019) Wu, Guo-Cheng; Baleanu, Dumitru; Deng, Zhen-Guo; Baleanu, Dumitru; Zeng, De-Qiang; 56389
New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly. Published under license by AIP Publishing.
Variational iteration method as a kernel constructive technique
(Elsevier Science inc, 2015) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Deng, Zhen-Guo
The variational iteration method newly plays a crucial role in establishing new integral equations. The Lagrange multipliers of the method serve kernel functions of the Volterra integral equations. A concept of an optimal integral equation is proposed. Then nonlinear examples are used to show the strategy's efficiency. (C) 2014 Elsevier Inc. All rights reserved.