Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 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: 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.