Uniform boundedness and stability of fractional state-dependent delayed systems and applications to complex neural networks

Liguang Xu, Hongxiao Hu and Danhua He

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 599-615

Abstract: In this article, the uniform boundedness and stability are investigated for a class of conformable fractional state-dependent delayed nonlinear systems. First, the definitions of generalized conformable fractional derivative and integral with subscripts are presented along with their properties, which improve and generalize the existing ones. Second, a conformable fractional exponential function inequality and a non-autonomous conformable fractional differential inequality are established, which can overcome the difficulties caused by fractional differential operators. Third, by combining the method of proof by contradiction with the Lyapunov method and the obtained inequalities, sufficient conditions are derived to ensure the uniform boundedness and stability of the addressed systems. Our results include some existing works on integer-order systems as special cases. Furthermore, as an application, the obtained theoretical results are applied to the quasi-synchronization problem of conformable fractional complex neural networks. Finally, examples are also provided to show the effectiveness of the theoretical results.

Keywords: Uniform boundedness; State-dependent delay; Conformable fractional nonlinear systems; Lyapunov method; Complex neural networks (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:599-615

DOI: 10.1016/j.matcom.2025.06.018

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