Finite-time synchronization of fully complex-valued neural networks with fractional-order

In this paper, without separating complex-valued neural networks into two real-valued systems, the finite-time synchronization is addressed for a class of fully complex-valued neural networks with fractional-order. Firstly, a new fractional-order differential inequality is established to improve some existing results in the real domain. Besides, to avoid the traditional separation method, the sign function of complex numbers is proposed and some properties about it are derived. Under the proposed sign function framework, by designing some novel and effective control schemes, constructing nontrivial Lyapunov functions and developing some new inequality methods in complex domain, several criteria of finite-time synchronization are derived and the settling-time of synchronization is effectively estimated. Finally, the effectiveness of the theoretical results is demonstrated by some numerical examples.