@Article{cmc.2020.011623,
AUTHOR = {Berat Karaagac, Kolade Matthew Owolabi, Kottakkaran Sooppy Nisar},
TITLE = {Analysis and Dynamics of Illicit Drug Use Described by  Fractional Derivative with Mittag-Leffler Kernel},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {65},
YEAR = {2020},
NUMBER = {3},
PAGES = {1905--1924},
URL = {http://www.techscience.com/cmc/v65n3/40146},
ISSN = {1546-2226},
ABSTRACT = {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.},
DOI = {10.32604/cmc.2020.011623}
}