Fractal Fractional Modelling of Social Media Addiction with Mittag generalized Decay Stability and Recovery Analysis (European Journal of Pure and Applied Mathematics, 2025)
Social media addiction impact mental health, social interaction, and productivity levels significantly. The addiction dynamics of this paper are modelled by stratifying the users into general users, mildly addicted, and highly addicted persons in light of recovery-based psychological treatment. This paper uses the fractional mathematical model, the fractal-fractional operator, and the Mittag-Leffler kernel to study addiction paths and recoveries. Reliability of the model presented is established through fixed-point theory and Ulam-Hyers stability. Numerical simulations are conducted to show the influence of fractional-order parameters on addiction and recovery. It gives an idea about how to intervene in an effective manner. Our findings will support the development of targeted rehabilitation programs and digital wellness policies.
Keywords: Fractional-order modelling; Fractal calculus; Unique solvability