FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

doi:10.1007/s10473-019-0611-x

Abstract

Abstract: The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that the delay feedback are bounded by similar functions. An application to a problem arising in neural network theory is provided showing that the equilibrium is Mittag-Leffler stable.

Key words: Hopfield neural network, Mittag-Leffler stability, Caputo fractional derivative, fractional Halanay inequality

CLC Number:

26A33

Nasser-eddine TATAR. FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY[J].Acta mathematica scientia,Series B, 2019, 39(6): 1605-1618.

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