Abstract
In this manuscript, we study the fractional compartmental model of drinking behavior with Atangana-Baleanu-Caputo (ABC) derivative. The fractional order model is divided into three different groups regarding their consumption in alcohol susceptible (nonconsumer), moderated drinkers and risk drinkers. We show the existence results and uniqueness of the solution by using the fixed point theory under the ABC derivative with fractional order. By using the modified Adams-Bashforth method we obtain the numerical solution of the fractional-order model. We use different values to obtain the numerical results of the fractional-order parameter to show its importance and provide important information about the drinking model.