Controllability of fractional-order directed complex networks

Abstract

This paper is a step forward to generalize the fundamentals of the conventional controllability in fractional-order complex networks. First, we discuss the existence of controllability theory of fractional-order complex networks. Furthermore, we propose stringent mathematical expression and controllable proof of fractional complex networks. Finally, three typical examples from the simplest network, the chain fractional-order network, to the Small-World network are presented to validate the correctness of the above theorem.