Sayooj Aby Jose, Raja Ramachandran, Dumitru Baleanu, Hasan S. Panigoro, Jehad Alzabut, Valentina E. Balas
In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor-corrector rule for the ABC-fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one. © 2022 John Wiley & Sons, Ltd.
Department of Mathematics, Alagappa University, Karaikudi, 630 004, India; Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India; Department of Mathematics, Cankaya University, Ankara, 06530, Turkey; Institute of Space Sciences, Bucharest, Magurele, Romania; Lebanese American University, Beirut, Lebanon; Biomathematics Research Group, Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango, 96119, Indonesia; Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia; Department of Industrial Engineering, OSTİM Technical University, Ankara, 06374, Turkey; Department of Automation and Applied Informatics, Aurel Vlacieu University of Arad, Arad, Romania
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