A Fractional-Order Peer Influence Mathematical Model

In this article, a fractional-order mathematical model is used to simulate peer influence using the Liouville–Caputo framework. Our model was made up of four states, which describe friends, negatively behaved friends, parental guidance, and positively behaved friends. We found the equilibrium points and also did the stability analysis to ascertain the conditions necessary for a stable solution. Again, we established the uniqueness, existence, and boundedness of our solution through the use of the Banach fixed point theorem and also checked for the global stability of our equilibrium points using the Lyapunov function. We finally conducted a numerical simulation with various parameters and fractional orders, demonstrating the effectiveness of our method. Our study revealed that the various fractional orders used have a great impact on the behavior of the model. In addition, we found that negatively behaved individuals have a greater influence on other individuals, so for us to curb or lower their associations and interactions, parental guidance must be intentionally increased. Our study contributes to the understanding and dynamics of peer influence through mathematical modeling.