Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel
- Berat Karaagac1, 2, Kolade Matthew Owolabi1, 3, *, Kottakkaran Sooppy Nisar4
1 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
2 Department of Mathematics Education, Faculty of Education, Adıyaman University, Adıyaman, Turkey.
3 Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
4 Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Al Kharj, Saudi Arabia.
* Corresponding Author: Kolade Matthew Owolabi. Email: koladematthewowolabi@tdtu.edu.vn.
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)
2 Department of Mathematics Education, Faculty of Education, Adıyaman University, Adıyaman, Turkey.
3 Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
4 Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Al Kharj, Saudi Arabia.
* Corresponding Author: Kolade Matthew Owolabi. Email: koladematthewowolabi@tdtu.edu.vn.
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)
Received 20 May 2020; Accepted 03 August 2020; Issue published 16 September 2020
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.
Keywords
Atangana-Baleanu fractional operator, illicit drug use, existence and uniqueness of solutions, stability analysis.
Cite This Article
Karaagac, B., Owolabi, K. M., Nisar, K. S. (2020). Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel. CMC-Computers, Materials & Continua, 65(3), 1905–1924.
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