Halanay inequality involving Caputo-Hadamard fractional derivative and application-Reference-Cited by-同舟云学术

Halanay inequality involving Caputo-Hadamard fractional derivative and application

Published:2022-01-06 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Kassim Mohammed D.¹^ORCID,Tatar Nasser-eddine²

Affiliation:

1. Department of Basic Engineering Sciences, College of Engineering , Imam Abdulrahman Bin Faisal University , P.O. Box 1982 , Dammam 34151 , Saudi Arabia

2. Department of Mathematics , King Fahd University of Petroleum and Minerals, Center for Intelligent Manufacturing and Robotics , Dhahran 31261 , Saudi Arabia

Abstract

AbstractA 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.

Publisher

Walter de Gruyter GmbH

Subject

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

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2021-0220/pdf

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