The Fractional Variable-Order Cucker-Smale Type Model for a Couple of Agents

The paper is devoted to the behaviour of fractional variable-order system with two agents. Interactions between agents are defined like in Cucker-Smale model but the memory is included by using the Grünwald-Letnikov fractional variable-order operator in the equation describing the velocity of agents. The condition for achieving a consensus for the considered model is formulated and the behaviour of the system is supported by numerical analysis.

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