Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 20Applications of Short Memory Fractional Differential Equations With Impulses(L and H Scientific Publishing, LLC, 2023) Wu, G.-C.; Baleanu, D.; Shiri, B.Dynamical systems’ behavior is sometimes varied with some impulse and sudden changes in process. The dynamics of these systems can not be modeled by previous concepts of derivative or fractional derivatives any longer. The short memory concept is a solution and a better choice for fractional modeling of such processes. We apply short memory fractional differential equations for these systems. We propose collocation methods based on piecewise polynomials to approximate solutions of these equations. We provide various examples to demonstrate the application of the short memory derivative for impulse systems and efficiency of the presented numerical methods. © 2023 L&H Scientific Publishing, LLC. All rights reservedArticle Citation - Scopus: 14Several Fractional Differences and Their Applications To Discrete Maps(L and H Scientific Publishing, LLC, 2015) Baleanu, D.; Zeng, S.-D.; Wu, G.-C.Several definitions of fractional differences are discussed. Their applications to fractional maps are compared. As an example, the logistic equation of integer order is discretized by these fractional difference methods. The comparative results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors. © 2015 L & H Scientific Publishing, LLC.Article Citation - WoS: 98Citation - Scopus: 121A Nonstandard Finite Difference Scheme for the Modeling and Nonidentical Synchronization of a Novel Fractional Chaotic System(Springer, 2021) Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A.The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy. © 2021, The Author(s).Article Citation - Scopus: 5Chaos Synchronization of the Fractional Rucklidge System Based on New Adomian Polynomials(L and H Scientific Publishing, LLC, 2017) Baleanu, D.; Huang, L.-L.; Wu, G.-C.The fractional Rucklidge system is a new kind of chaotic models which hold the feature of memory effects and can depict the long history interactions. A numerical formula is proposed by use of the fast Adomian polynomials. Chaotic behavior are discussed and the Poincare sections are given for various fractional cases. It's also applied in chaos synchronization of the fractional system. © 2017 L & H Scientific Publishing, LLC.