Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks.

Abstract Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks are investigated in this paper. The model of fractional-order inertial neural network is proposed, which is more general and less conservative than the integer-order inertial neural network. Two lemmas on the composition properties of Riemann-Liouville fractional-order derivative and integral are given. Based on the composition properties of Riemann-Liouville fractional-order derivative, the original inertial system is transferred into conventional system through the proper variable substitution. Serval novel and effective feedback controllers are proposed for different cases of fractional-order time-delayed inertial neural networks, such that synchronization between the salve system and the master system can be achieved. In addition, stability conditions for a class of fractional-order time-delayed inertial neural networks are derived. Furthermore, three numerical examples are provided to show the validity and feasibility of the approaches. [ABSTRACT FROM AUTHOR]