Abstract
This study investigates the synchronization of coupled fractional-order Markovian reaction-diffusion neural networks (MRDNNs) with partially unknown transition rates. The novelty of this work is mainly reflected in three aspects: First, this study incorporates the Markovian switching model and reaction-diffusion term into a fractional-order system, which is a challenging and under-explored issue in existing literature, and effectively addresses the synchronization problem of fractional-order MRDNNs by introducing a continuous frequency distribution model of the fractional integrator. Second, it derives a new set of sufficient synchronization conditions with reduced conservatism; by utilizing the (extended) Wirtinger inequality and delay-partitioning techniques, abundant free parameters are introduced to significantly broaden the solution range. Third, it proposes an LMI-based optimal synchronization design by establishing an efficient offline optimization framework with semidefinite constraints, and achieves the precise solution of control gains. Finally, numerical simulations are conducted to validate the effectiveness of the proposed method.