3rd TAGRA

Mobile gaming addiction has emerged as a significant behavioural problem which could be investigated mathematically through modelling techniques akin to those used for transmission of diseases in a population. In this paper, we propose a Takagi-Sugeno fuzzy fractal-fractional model to describe the dynamics of PUBG Mobile addiction via a system of five compartments: susceptible, exposed, addicted, treated, and recovered players. The nonlinear interaction that gives rise to the emergence of addicted players is modelled by means of an exact sector-based Takagi-Sugeno model, maintaining the original nonlinear system in the given state domain. This model is further generalized to a fractal-fractional system with two independent orders to incorporate memory and fractality effects in the system dynamics. The mathematical characteristics of the proposed model are explored through results on existence and uniqueness, positivity, boundedness, and Ulam-Hyers stability. For numerical solution of the fractal-fractional model, a piecewise Lagrange interpolation technique is utilized. To calibrate the model, an eighteen-months series of PUBG Mobile daily active user data from January 2024 to June 2025 is analysed. The proposed model is then estimated by fitting the model directly to the actual data by jointly optimizing the model rate parameters along with the two orders of the derivatives. The resulting fractal–fractional fuzzy framework is compared to the classical and fractional models using the same real dataset. It is evident from the numerical findings that the fractal–fractional model performs better with respect to the observed data and captures the slowly changing nature of the PUBG Mobile users.