ANALYSIS OF SOCIAL MEDIA ADDICTION MODEL WITH SINGULAR OPERATOR

Abstract

In this work, we study a dynamic model of social media addiction. Addiction to social media is a behavioral addiction that is very complex in nature. To study such kinds of complex behavior, the fractional-order operators are very useful due to their memory nature. Considering all these facts, we consider the fractional and fractal-fractional operators with a singular kernel to investigate the social media addiction model. This paper’s main aim is to demonstrate the importance of non-classical-order derivatives in the investigation of the social media addiction model. First, we propose the model using Caputo fractional derivative and present some basic mathematical computations. The existence condition for a solution of the model system is presented via fixed-point theory. Furthermore, the behavior of the social media addiction model is examined using the fractal-fractional concept with the Caputo operator, which, due to its memory effect, is very effective in modeling. The existence and uniqueness of the solution are investigated using fixed point theory. Ulam–Hyers stability is demonstrated using nonlinear functional analysis. We demonstrate the simulated numerical results graphically for the proposed models via numerical methods based on Lagrange polynomial interpolation. The results are plotted for choices of arbitrary-order parameter values. Based on our findings, we can say the fractal-fractional operators provide more realistic information about the complexity of the dynamics of the social media addiction model.