Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 38Citation - Scopus: 40A New Application of the Fractional Logistic Map(Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; MatematikThe 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.Article Citation - WoS: 134Citation - Scopus: 147Discrete Chaos in Fractional Sine and Standard Maps(Elsevier, 2014) Baleanu, Dumitru; Zeng, Sheng-Da; Wu, Guo-ChengFractional 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.Article Citation - WoS: 22Citation - Scopus: 26Discrete Fractional Diffusion Equation of Chaotic Order(World Scientific Publ Co Pte Ltd, 2016) Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; Wu, Guo-ChengDiscrete 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.Article Citation - WoS: 31Citation - Scopus: 36Mittag-Leffler Function for Discrete Fractional Modelling(Elsevier, 2016) Baleanu, Dumitru; Zeng, Sheng-Da; Luo, Wei-Hua; Wu, Guo-ChengFrom 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.Article Citation - WoS: 4Citation - Scopus: 5Lattice Fractional Diffusion Equation of Random Order(Wiley, 2017) Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; Wu, Guo-ChengThe 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.Article Citation - WoS: 64Citation - Scopus: 82Discrete Fractional Diffusion Equation(Springer, 2015) Baleanu, Dumitru; Zeng, Sheng-Da; Deng, Zhen-Guo; Wu, Guo-ChengThe 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.Article Citation - WoS: 80Citation - Scopus: 79Lattice Fractional Diffusion Equation in Terms of a Riesz-Caputo Difference(Elsevier, 2015) Baleanu, Dumitru; Deng, Zhen-Guo; Zeng, Sheng-Da; Wu, Guo-ChengA 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.