Fractional discrete-time of Hegselmann-Krause's type consensus model with numerical simulations

The leader-following consensus problem of fractional-order multi-agent discrete-time systems is considered. In the system, interactions between opinions are defined like in the classical Hegselmann-Krause models but the memory is included by taking the fractional-order discrete-time operator on the left-hand side of the nonlinear system. In the paper we investigate various models for the dynamics of discrete-time fractional order opinions by analytical methods as well as by computer simulations.