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A neutral fractional Halanay inequality and application to a Cohen-Grossberg neural network system
  • Mohammed Kassim,
  • Nasser-eddine Tatar
Mohammed Kassim
Imam Abdulrahman Bin Faisal University
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Nasser-eddine Tatar
King Fahd University of Petroleum and Minerals
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Abstract

We extend the well-known Halanay inequality to the fractional order case in presence of distributed delays and delays of neutral type (in the fractional derivative). Both the discrete and distributed neutral delays are investigated. It is proved that solutions decay toward zero in a Mittag-Leffler manner under some rather general conditions. Some large classes of kernels and examples satisfying our assumptions are provided. We apply our findings to prove Mittag-Leffler stability for solutions of fractional neutral network systems of Cohen-Grossberg type.

Peer review status:ACCEPTED

20 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
22 Feb 2021Submission Checks Completed
22 Feb 2021Assigned to Editor
27 Feb 2021Reviewer(s) Assigned
27 Feb 2021Review(s) Completed, Editorial Evaluation Pending
09 Mar 2021Editorial Decision: Revise Minor
20 Mar 20211st Revision Received
21 Mar 2021Submission Checks Completed
21 Mar 2021Assigned to Editor
21 Mar 2021Editorial Decision: Accept