Halanay inequality involving Caputo-Hadamard fractional derivative and application

Mohammed D. Kassim*, Nasser Eddine Tatar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)2663-2675
Number of pages13
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Issue number7
StatePublished - 1 Nov 2023

Bibliographical note

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


  • 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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