Global Mittag-Leffler Projective Synchronization of Distinct Fractional-order Delayed Neural Networks with Inconsistent Orders and Interaction Terms via integral Sliding Mode Control

Abstract This work focuses on the global Mittag–Leffler projective synchronization (GMLPS) of distinct fractional-order delayed neural networks (FODNNs) with inconsistent orders and interaction terms. Initially, a delayed fractional-order (FO) integral sliding surface is made by embedding the FO gradient fed into the controller, facilitating the formulation of a synchronous error system. Subsequently, a delayed sliding mode controller (SMC) is formulated using the sliding mode control theory to guarantee the occurrence of the sliding motion. Furthermore, error systems are shown to converge to the predefined sliding surface, enabling sliding motion through the fractional Lyapunov direct approach and the Razumikhin method. Novel criteria are established to achieve the GMLPS for distinct FODNNs with inconsistent orders and interaction terms. Finally, numerical experiments are exploited to highlight the performance of the obtained outcomes.