ANALYZING SOCIAL MEDIA ADDICTION: A FRACTIONAL-ORDER MODEL

The emergence of excessive social media use has raised significant concerns in the twenty-first century, necessitating urgent attention to mitigate potential adverse consequences. To address this challenge, a range of preventive strategies, such as advertising campaigns and awareness programs, are being utilized to highlight the negative impacts of digital technologies. Employing advanced mathematical methods and terminology can significantly contribute to encouraging healthier lifestyles and preventing-related health problems. Consequently, this paper investigates the fractional-order mathematical modeling to comprehend social media addiction across various user classes, such as non-users, exposed individuals, social media users, professionals, and addicted users. In the realm of qualitative analysis, the study establishes the existence, uniqueness, non-negativity, and boundedness of solutions of the model. Within the framework of the fractional-order model, essential elements are identified, including the equilibrium points and the fundamental reproduction number. To evaluate the stability of the social media addiction model across these user categories, the study employs the fractional Routh–Hurwitz criterion. Furthermore, the research proves the global asymptotic stability of all equilibria through the development of inventive Lyapunov functions. Additionally, the numerical simulation of the fractional-order model provides a comprehensive understanding of the dynamics of social media addiction within the distinct user classes.