TY - EJOU AU - Karaagac, Berat AU - Owolabi, Kolade Matthew AU - Nisar, Kottakkaran Sooppy TI - Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel T2 - Computers, Materials \& Continua PY - 2020 VL - 65 IS - 3 SN - 1546-2226 AB - Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society. For this reason, illicit drug use and related crimes are the most significant criminal cases examined by scientists. This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. Also, in this work, the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence. Then the stability analysis for both disease-free and endemic equilibrium states is conducted. A numerical scheme based on the known Adams-Bashforth method is designed in fractional form to approximate the novel Atangana-Baleanu fractional operator of order 0 < α ≤ 1. Finally, numerical simulation results based on different values of fractional order, which also serve as control parameter, are presented to justify the theoretical findings. KW - Atangana-Baleanu fractional operator KW - illicit drug use KW - existence and uniqueness of solutions KW - stability analysis DO - 10.32604/cmc.2020.011623