Finite-time stability of fractional-order quaternion-valued memristive neural networks with time delay

This study addresses the finite-time stability (FTS) problem of fractional-order quaternion-valued memristive neural networks (FQMNNs) with time delay. Firstly, by leveraging set-valued mapping, differential inclusion, and contracting mapping principle, the sufficient condition is provided to assure the existence and uniqueness of the equilibrium point. Secondly, given the fractional order differential inequality and Gronwall inequality, finite-time stability (FTS) criterion is obtained for the delayed FQMNNs with the fractional order between 0 and 1. Additionally, a sufficient condition is proposed to guarantee the FTS of FQMNNs with the fractional order between 1 and 2. Compared with existing results, this study not only extends the fractional order between and 2, but also incorporates quaternions, which significantly enhances the FTS theory. Finally, two numerical examples demonstrate the practicality of the obtained results.