Finite-time synchronization of delayed fractional-order heterogeneous complex networks.

This paper is devoted to exploring the finite-time (FET) synchronization problem of time-varying delay fractional-order (FO) coupled heterogeneous complex networks (TFCHCNs) with external interference via a discontinuous feedback controller. Firstly, we propose a novel Lemma which is useful for discussing the FET stability and synchronization problem of FO systems. Secondly, based on the proposed Lemma, a discontinuous feedback controller is designed to guarantee the FET synchronization of TFCHCNs with external interference. Moreover, the upper bound of settling-time function is obtained. Finally, two simulation examples are provided to verify the practicability of our findings.