A Fractional Model of an Effect of Awareness Programs by Media on Binge Drinking Model with Mittag-Leffler Kernel

Year 2020, Volume: 8 Issue: 1, 175 - 184, 15.04.2020

Sumeyra Ucar Necati Özdemir

Abstract

Alcoholism is one of the problems that societies have not been able to find a solution for a long time. Today, over 2 billions of people consume alcohol and it is estimated that approximately 76 million of these people are addicted. In this study, an alcoholism model is broadly researched with the help of AB derivative. The existence and uniqueness of the drinking model solutions together with the stability analysis is demonstrated through Banach fixed point theorem. The special solution of the model is investigated using the Sumudu transformation and following that, a set of numeric graphics are given for different fractional orders with the intention of showing the effectiveness of fractional derivative. Hence, it is obtained that while awareness programs driven by media increases, the number of heavy drinkers decreases.

Keywords

Fractional differential equations, Atangana-Baleanu derivative, mathematical model

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