학술논문
Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative.
Document Type
Article
Author
Source
Subject
*SUBSTANCE abuse
*FIXED point theory
*BASIC reproduction number
*INTEGRAL operators
*NONLINEAR theories
*HAMILTONIAN graph theory
*DYNAMICAL systems
*BEES algorithm
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Language
ISSN
0170-4214
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. [ABSTRACT FROM AUTHOR]