AUTHOR=Shutaywi Meshal , Rehman Ziad Ur , Shah Zahir , Vrinceanu Narcisa , Jan Rashid , Deebani Wejdan , Dumitrascu Oana 

TITLE=Modeling and analysis of the addiction of social media through fractional calculus

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=9

YEAR=2023

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1210404

DOI=10.3389/fams.2023.1210404

ISSN=2297-4687

ABSTRACT=<p>Social media addiction (SMA) is the excessive use of social media platforms, resulting in negative consequences for individuals. It is characterized by an uncontrollable urge to use social media, leading to negative effects in human's life. This study aims to construct a mathematical model to conceptualize the transmission dynamics of SMA and explore the underlying mechanisms of this harmful addiction in the framework of fractional derivative. The fundamentals of fractional calculus are listed for examining the model. Equilibrium points are identified, and the reproduction parameter R<sub>0</sub> is computed to understand the dynamics of SMA spread. Stability analysis of the equilibria is performed, and the impact of various input parameters is numerically investigated. The existence and uniqueness of the proposed SMA model are demonstrated through simulations, which also study the intricate dynamics with respect to different input factors. To develop effective control strategies, the system's dynamical behavior is examined, and the influence of fractional derivative order on fluctuations is explored. This research offers a range of suggestions aimed at reducing the occurrence of social media addiction.</p>