A new analysis for fractional rumor spreading dynamical model in a social network with Mittag-Leffler law.

Rumor plays a key role in social interaction, and its spreading has a notable influence on human lives. In this work, we study the rumor spreading dynamical model in a social network associated with the Atangana-Baleanu derivative of non-integer order. A deterministic model of the rumor spreading is studied. The solution of the rumor spreading dynamical model is obtained by employing an iterative scheme. Additionally, existence and uniqueness of the solution are discussed by employing the Picard-Lindelöf scheme. The effect of the order of AB fractional derivative on ignorants, spreaders, and stiflers is analyzed. Finally, to represent the obtained results, some numerical simulations are shown via graphs.