Halanay inequality involving Caputo-Hadamard fractional derivative and application

Mohammed D. Kassim; Nasser Eddine Tatar

doi:10.1515/ijnsns-2021-0220

Halanay inequality involving Caputo-Hadamard fractional derivative and application

Mohammed D. Kassim^*, Nasser Eddine Tatar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided. This needs the preparation of several lemmas on properties of the Hadamard derivative and some basic fractional differential problems with this kind of derivative. The obtained result is then applied to a Hopfield neural network system to discuss its stability.

Original language	English
Pages (from-to)	2663-2675
Number of pages	13
Journal	International Journal of Nonlinear Sciences and Numerical Simulation
Volume	24
Issue number	7
DOIs	https://doi.org/10.1515/ijnsns-2021-0220
State	Published - 1 Nov 2023

Bibliographical note

Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.

Keywords

Hadamard derivative
Halanay inequality
Hopfield neural network
Mittag-Leffler stability

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Computational Mechanics
Modeling and Simulation
Engineering (miscellaneous)
Mechanics of Materials
General Physics and Astronomy
Applied Mathematics

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10.1515/ijnsns-2021-0220

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abstract = "A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided. This needs the preparation of several lemmas on properties of the Hadamard derivative and some basic fractional differential problems with this kind of derivative. The obtained result is then applied to a Hopfield neural network system to discuss its stability.",

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author = "Kassim, {Mohammed D.} and Tatar, {Nasser Eddine}",

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T1 - Halanay inequality involving Caputo-Hadamard fractional derivative and application

AU - Kassim, Mohammed D.

AU - Tatar, Nasser Eddine

PY - 2023/11/1

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N2 - A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided. This needs the preparation of several lemmas on properties of the Hadamard derivative and some basic fractional differential problems with this kind of derivative. The obtained result is then applied to a Hopfield neural network system to discuss its stability.

AB - A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided. This needs the preparation of several lemmas on properties of the Hadamard derivative and some basic fractional differential problems with this kind of derivative. The obtained result is then applied to a Hopfield neural network system to discuss its stability.

KW - Hadamard derivative

KW - Halanay inequality

KW - Hopfield neural network

KW - Mittag-Leffler stability

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JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

IS - 7

ER -

Halanay inequality involving Caputo-Hadamard fractional derivative and application

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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