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This paper investigates the global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays. First, the model of fractional-order inertial memristive neural network with time-varying delays is proposed, which is more universal and less conservative than the integer-order inertial memristive neural network with time-varying delays. Second, one lemma about the compound property of Caputo fractional derivative and integral is given. According to the compound property of Caputo fractional derivative and appropriate variable substitution, the original inertial memristive system translates a routine inertial memristive system. And, using the Filippov discontinuous theory, Lyapunov stability theory, and Mittag-Leffler convergence, several sufficient conditions are derived to ensure the global Mittag-Leffler synchronization of Caputo fractional-order inertial memristive neural networks. An effective feedback controller is proposed for fractional-order inertial memristive neural networks with time-varying delays, such that the global Mittag-Leffler synchronization between the slave system and the master system can be achieved. Finally, a simulation example is given to verify the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, from the classical short memory principle under Grünwald-Letnikov definition, several novel short memory principles are presented and investigated. On one hand, the classical principle is extended to Riemann-Liouville and Caputo cases. On the other hand, a special kind of principles are formulated by introducing a discrete argument instead of the continuous time, resulting in principles with fixed memory length or fixed memory step. Apart from these, several interesting properties of the proposed principles are revealed profoundly. [ABSTRACT FROM AUTHOR]