Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (6): 1605-1618.doi: 10.1007/s10473-019-0611-x

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FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

Nasser-eddine TATAR   

  1. King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, 31261, Saudi Arabia
  • Received:2018-06-28 Revised:2018-11-17 Online:2019-12-25 Published:2019-12-30
  • Supported by:
    Supported by King Abdulaziz City of King Abdulaziz City of Science and Technology (KACST) under the National Science, Technology and Innovation Plan (NSTIP), Project No. 15-OIL4884-0124.

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
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