Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations

This paper studies the dynamics of an opinion formation model with a leader associated with a system of fractional differential equations. We applied the concept of $\alpha$-exponential stability and the uniqueness of equilibrium to show the consensus of the followers with the leader. A sufficient condition for the consensus is obtained for both fractional formation models with and without time-dependent external inputs. Moreover, numerical results are provided to illustrate the dynamical behavior.