Behaviour of the fractional Cucker-Smale type model for a couple of agents

The behaviour of fractional-order systems with two agents is considered. In the paper, interactions between agents are defined like in Cucker-Smale models, where equations related to the position are the ordinary differential equations and velocities of agents are described by fractional differential equations. It allows us to take into account the memory that is included by taking the fractional-order, what seems to significantly improve the classical model. The conditions for achieving the consensus for the considered models are formulated based on the stability analysis of the appropriate linear systems. Finally, the behaviours of systems are illustrated by examples.