Chaos synchronization between two different fractional systems of Lorenz family.
Matouk, A.E. (2009)
Mathematical Problems in Engineering
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Matouk, A.E. (2009)
Mathematical Problems in Engineering
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Zakia Hammouch, Toufik Mekkaoui (2014)
Nonautonomous Dynamical Systems
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In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the effectiveness of the proposed methods.
Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)
Mathematical Problems in Engineering
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Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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Jianbing Hu, Hua Wei, Lingdong Zhao (2015)
Kybernetika
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In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.
Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...
Rajneesh Kumar, Poonam Sharma (2016)
Curved and Layered Structures
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This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative...
B. Martić (1964)
Matematički Vesnik
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Masayoshi Hata (2005)
Acta Arithmetica
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Li, Ming, Lim, S.C., Chen, Shengyong (2011)
Mathematical Problems in Engineering
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Datsko, Bohdan, Luchko, Yuri (2012)
Mathematica Balkanica New Series
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MSC 2010: 26A33, 34D05, 37C25 In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to...