Modeling and analysis of the dynamics of an excessive gambling problem with modified fractional operator

This work introduces a fractional-order model of gambling addiction using the modified Atangana-Baleanu-Caputo operator. We establish solution existence/uniqueness, derive the reproduction number R0, and analyze stability. Numerical results demonstrate how fractional order υ influences addiction dynamics. The model identifies key intervention parameters through sensitivity analysis. The optimal control strategy is proposed to reduce progression to addiction. These approaches provide new tools for understanding and managing problem gambling behaviors.