Fractional Opinion Formation Models with Leadership

Abstract

The paper studies two types of fractional opinion formation models with leader: the Hegselmann–Krause and the Cucker–Smale. We aim to design an optimal control strategy for the systems to reach a consensus. A numerical scheme, based on Grunwald–Letnikov approximation of the Caputo ¨ fractional derivative, is proposed for solving the fractional optimal control problem. The effectiveness of the proposed control strategy is illustrated by examples.