FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

doi:10.1007/s10473-019-0611-x

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1605-1618.doi: 10.1007/s10473-019-0611-x

FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

Nasser-eddine TATAR

King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, 31261, Saudi Arabia

收稿日期:2018-06-28 修回日期:2018-11-17 出版日期:2019-12-25 发布日期:2019-12-30
作者简介:Nasser-eddine TATAR,E-mail:tatarn@kfupm.edu.sa
基金资助:
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.

FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

Nasser-eddine TATAR

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.

摘要/Abstract

摘要： 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.

关键词: Hopfield neural network, Mittag-Leffler stability, Caputo fractional derivative, fractional Halanay inequality

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

中图分类号:

26A33

Nasser-eddine TATAR. FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY[J]. 数学物理学报(英文版), 2019, 39(6): 1605-1618.

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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FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY

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