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: 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.