Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Bifurcations, Hidden Chaos and Control in Fractional Maps(MDPI AG, 2020) Pham, Viet-Thanh; Ouannas, Adel; Almatroud, Othman Abdullah; Baleanu, Dumitru; Alsawalha, Mohammad Mossa; Khennaoui, Amina Aicha; Huynh, Van VanArticle 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: 3Citation - Scopus: 5Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model(Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, IramThis manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.Article Citation - WoS: 6Citation - Scopus: 7Reprint Of: Chaos Synchronization of the Discrete Fractional Logistic Map(Elsevier, 2015) Baleanu, Dumitru; Wu, Guo-ChengIn this paper, master slave synchronization for the fractional difference equation is studied with a nonlinear coupling method. The numerical simulation shows that the designed synchronization method can effectively synchronize the fractional logistic map. The Caputo-like delta derivative is adopted as the difference operator. (C) 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 153Citation - Scopus: 162Chaos Synchronization of the Discrete Fractional Logistic Map(Elsevier, 2014) Baleanu, Dumitru; Wu, Guo-ChengIn this paper, master-slave synchronization for the fractional difference equation is studied with a nonlinear coupling method. The numerical simulation shows that the designed synchronization method can effectively synchronize the fractional logistic map. The Caputo-like delta derivative is adopted as the difference operator. (C) 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 11Bifurcations, Hidden Chaos and Control in Fractional Maps(Mdpi, 2020) Almatroud, Othman Abdullah; Khennaoui, Amina Aicha; Alsawalha, Mohammad Mossa; Baleanu, Dumitru; Van Van Huynh; Viet-Thanh Pham; Ouannas, Adel; Pham, Viet-thanh; Huynh, Van VanRecently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.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: 64Citation - Scopus: 77Image Encryption Technique Based on Fractional Chaotic Time Series(Sage Publications Ltd, 2016) Baleanu, Dumitru; Lin, Zhen-Xiang; Wu, Guo-ChengChaos in discrete fractional maps has been reported very recently. In this study, the chaotic time series of fractional order is used in the scrambling technique and a novel image encryption scheme is designed. The fractional difference order and the chaotic coefficient play crucial roles in controlling chaotic behaviors. The encrypted results are analyzed, which shows that the encryption scheme is highly secure.Article Citation - WoS: 39Citation - Scopus: 48Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors(Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; Gómez-Aguilar, José Francisco; Pérez, Jesús Emmanuel SolísThis paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.