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

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