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Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. (English) Zbl 1331.34154
Summary: In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.

##### MSC:
 34K37 Functional-differential equations with fractional derivatives 34K20 Stability theory of functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics
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