https://doi.org/10.1140/epjp/s13360-025-06840-w
Regular Article
Mittag–Leffler and asymptotic adaptive projective synchronization of fractional inertial neural networks in quaternion field
1
School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, 175005, Kamand, Mandi, Himachal Pradesh, India
2
CITMAga, Department of Statistics, Mathematical Analysis and Optimization, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
Received:
30
June
2025
Accepted:
8
September
2025
Published online:
21
September
2025
This paper investigates the problems of Mittag–Leffler projective synchronization (MLPS) and asymptotic adaptive projective synchronization (AAPS) in fractional quaternion-valued inertial neural networks (FQVINNs) subject to parametric uncertainties. To facilitate the analysis, the original FQVINN model is reformulated into an equivalent fractional system through an appropriate variable transformation. Two synchronization strategies are proposed: a quaternion-valued feedback controller is designed to realize MLPS, while a fractional adaptive controller is developed to achieve AAPS. By employing tools from fractional differential inequality theory and Lyapunov stability analysis, sufficient conditions for the synchronization of FQVINNs are rigorously established. The effectiveness of the proposed control schemes is demonstrated through a numerical example, which confirms the theoretical predictions and highlights the practical applicability of the methods.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
