On analysis of a nonlinear fractional system for social media addiction involving Atangana–Baleanu–Caputo derivative

Advances in Difference Equations

article

Kongson, Jutarat¹  Sudsutad, Weerawat³  Thaiprayoon, Chatthai¹  Alzabut, Jehad⁵  Tearnbucha, Chutarat⁴ 

[1] Department of Mathematics, Faculty of Science, Burapha University;Center of Excellence in Mathematics;Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok;Department of General Education, Faculty of Science and Health Technology, Navamindradhiraj University;Deparment of Mathematics and General Sciences, Prince Sultan University;Group of Mathematics, Faculty of Engineering, Ostim Technical University

关键词: Atangana–Baleanu–Caputo fractional derivative;    Fixed-point theorems;    Numerical simulations;    Social media addiction;    Ulam–Hyers stability;   

DOI  :  10.1186/s13662-021-03515-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

A mathematical model for the dynamic systems of$\mathbb{SMA}$ involving the$\mathbb{ABC}$ -fractional derivative is considered in this manuscript. We examine the basic reproduction number and analyze the stability of the equilibrium points. We prove the theoretical results of the existence and Ulam’s stability of the solutions for the proposed model using fixed point theory and nonlinear analytic techniques. Using the Adams type predictor–corrector rule for the$\mathbb{ABC}$ -fractional integral operator, a numerical scheme is devised for obtaining the approximate solution of the proposed model. Different numerical plots corresponding to various fractional orders are presented. In addition, we demonstrate a numerical simulation for the transmission of social media addiction in two cases with the basic reproduction numbers greater than and less than one.

【 授权许可】

CC BY