Finite-Time Synchronization of Discontinuous Fractional-Order Complex Networks With Delays

This paper considers the delay-related finite-time synchronization issue for fractional-order delayed complex networks (FODCNs) with discontinuous activations. Firstly, a novel fractional-order differential inequality with delay is derived based on the properties of Laplace transforms and Mittag-Leffler functions. In addition, with the aid of the constructed differential inequality, two new delay-related fractional-order finite-time convergence principles (FOFTCPs) is obtained. Furthmore, under the framework of Filippov's solution, a control protocol without delay is constructed to achieve the synchronization in infinite time for FODCNs. Finally, the effectiveness and validity of the proposed results are demonstrated through two numerical examples.