Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative. (15th November 2022)

• Record Type: Journal Article
• Authors: Jose, Sayooj Aby; Ramachandran, Raja; Baleanu, Dumitru; Panigoro, Hasan S.; Alzabut, Jehad; Balas, Valentina E.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 5(2023)
• Page Start: 5060
• Page End: 5085
• Publication Date: 2022-11-15
• Subjects: Atangana‐Baleanu‐Caputo derivative -- mathematical modeling -- reproduction number -- stability analysis; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8818
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.