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Decentralized adaptive strategies for synchronization of fractional-order complex networks

This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling. Based on local information among neighboring nodes, two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively. By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques, Mittag-Leffler function, and Laplace transform, two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws. Finally, two numerical examples are given to verify the theoretical results.