Optimal control and dynamic analysis of a new Atangana–Baleanu fractional rumor dissemination model involving media

Abstract

In recent years, how to control the spreading of rumors effectively has been one of the public hot issues. Mathematical models can provide quantitative analysis and decision support for this problem. In this paper, a rumor dissemination model with the Atangana–Baleanu fractional derivative in social networks is established, which includes the influence of authoritative media reports and the transformation mechanism of media. The basic properties of the solution for the considered system and the Ulam stability of the system are verified. In order to minimize the cost of controlling rumors, a real-time optimal control model is also proposed by using the Pontryagins maximum principle. At last, numerical simulation results are given to analyze the impacts of different parameters on the Atangana–Baleanu fractional rumor dissemination model, which indicates that our model is realistic and effective.