TY - JOUR
T1 - Halanay inequality involving ψ-Caputo derivative and application to a neural network system
AU - Kassim, Mohammed D.
AU - Tatar, Nasser Eddine
N1 - Publisher Copyright:
© Diogenes Co.Ltd 2025.
PY - 2025/12
Y1 - 2025/12
N2 - The well-known Halanay inequality is generalized here to the fractional-order case. We investigate this inequality in presence of a generalized Caputo fractional derivative in addition to discrete and distributed delays of not necessarily convolution type. The obtained result is then applied to a Hopfield Neural Network system to discuss its stability. This needs proving various lemmas on properties of the considered generalized Caputo derivative. We prove that solutions decay as a Mittag-Leffler function composed with a power function.
AB - The well-known Halanay inequality is generalized here to the fractional-order case. We investigate this inequality in presence of a generalized Caputo fractional derivative in addition to discrete and distributed delays of not necessarily convolution type. The obtained result is then applied to a Hopfield Neural Network system to discuss its stability. This needs proving various lemmas on properties of the considered generalized Caputo derivative. We prove that solutions decay as a Mittag-Leffler function composed with a power function.
KW - Generalized Caputo-type derivative (primary)
KW - Halanay inequality
KW - Hopfield neural network system
KW - Mittag-Leffler stability
UR - https://www.scopus.com/pages/publications/105018336583
U2 - 10.1007/s13540-025-00452-y
DO - 10.1007/s13540-025-00452-y
M3 - Article
AN - SCOPUS:105018336583
SN - 1311-0454
VL - 28
SP - 2774
EP - 2798
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 6
ER -