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 Grünwald–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.