Browsing by Author "Zeng, Sheng-Da"

Now showing 1 - 9 of 9

Citation - WoS: 204
Citation - Scopus: 237
Chaos Analysis and Asymptotic Stability of Generalized Caputo Fractional Differential Equations
(Pergamon-elsevier Science Ltd, 2017) Wu, Guo-Cheng; Zeng, Sheng-Da; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi-analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis. (C) Elsevier Ltd. All rights reserved.
Citation - WoS: 133
Citation - Scopus: 145
Discrete Chaos in Fractional Sine and Standard Maps
(Elsevier, 2014) Baleanu, Dumitru; Zeng, Sheng-Da; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional standard and sine maps are proposed by using the discrete fractional calculus. The chaos behaviors are then numerically discussed when the difference order is a fractional one. The bifurcation diagrams and the phase portraits are presented, respectively. (C) 2013 Elsevier B.V. All rights reserved.
Citation - WoS: 64
Citation - Scopus: 81
Discrete Fractional Diffusion Equation
(Springer, 2015) Baleanu, Dumitru; Zeng, Sheng-Da; Deng, Zhen-Guo; Wu, Guo-Cheng; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 21
Citation - Scopus: 24
Discrete Fractional Diffusion Equation of Chaotic Order
(World Scientific Publ Co Pte Ltd, 2016) Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 86
Citation - Scopus: 94
Finite-Time Stability of Discrete Fractional Delay Systems: Gronwall Inequality and Stability Criterion
(Elsevier, 2018) Baleanu, Dumitru; Zeng, Sheng-Da; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result. (c) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 80
Citation - Scopus: 79
Lattice Fractional Diffusion Equation in Terms of a Riesz-Caputo Difference
(Elsevier, 2015) Baleanu, Dumitru; Deng, Zhen-Guo; Zeng, Sheng-Da; Wu, Guo-Cheng; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 4
Citation - Scopus: 5
Lattice Fractional Diffusion Equation of Random Order
(Wiley, 2017) Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 30
Citation - Scopus: 35
Mittag-Leffler Function for Discrete Fractional Modelling
(Elsevier, 2016) Baleanu, Dumitru; Zeng, Sheng-Da; Luo, Wei-Hua; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta's sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function. (C) 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
Citation - WoS: 37
Citation - Scopus: 39
A New Application of the Fractional Logistic Map
(Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The fractional chaotic map started to be applied in physics and engineering to properly treat some real-world phenomena. A shuffling method is proposed based on the fractional logistic map. The fractional difference order is used as a key. An image encryption scheme is designed by using the XOR operation and the security analysis is given. The obtained results demonstrate that the fractional difference order makes the encryption scheme highly secure.