Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 90Citation - Scopus: 95Finite-Time Stability of Discrete Fractional Delay Systems: Gronwall Inequality and Stability Criterion(Elsevier, 2018) Baleanu, Dumitru; Zeng, Sheng-Da; Wu, Guo-ChengThis 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.Article Citation - WoS: 211Citation - Scopus: 242Chaos Analysis and Asymptotic Stability of Generalized Caputo Fractional Differential Equations(Pergamon-elsevier Science Ltd, 2017) Wu, Guo-Cheng; Zeng, Sheng-Da; Baleanu, DumitruThis 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.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.