Fixed-Time Synchronization for Fractional-Order Cellular Inertial Fuzzy Neural Networks with Mixed Time-Varying Delays

Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category of fractional-order cellular-inertial fuzzy neural networks (FCIFNNs) that involve mixed time-varying delays (MTDs), including both discrete and distributed delays. Firstly, we establish an appropriate transformation variable to reformulate FCIFNNs with MTD into a differential first-order system. Then, utilizing the finite-time stability (FETS) theory and Lyapunov functionals (LFs), we establish some new effective criteria for achieving FDTS of the response system (RS) and drive system (DS). Eventually, we offer two numerical examples to display the effectiveness of our proposed synchronization strategies. Moreover, we also demonstrate the benefits of our approach through an application in image encryption.