Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays.

*(English)*Zbl 1331.34154Summary: 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 |

##### Keywords:

finite-time stability; fractional-order; complex-valued neural networks; memristor; time delays
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\textit{R. Rakkiyappan} et al., Nonlinear Dyn. 78, No. 4, 2823--2836 (2014; Zbl 1331.34154)

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