### Synchronization of chaotic fractional-order WINDMI systems via linear state error feedback control.

Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)

Mathematical Problems in Engineering

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Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)

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.

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...

Zhou, Ping, Kuang, Fei (2011)

Discrete Dynamics in Nature and Society

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B. Martić (1964)

Matematički Vesnik

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Masayoshi Hata (2005)

Acta Arithmetica

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Helena Musielak (1973)

Colloquium Mathematicae

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Branislav Martić (1973)

Publications de l'Institut Mathématique

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