Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems IV
Guest Editors: Yeliz Karaca, Dumitru Baleanu, Majaz Moonis, Yu-Dong Zhang and Osvaldo Gervasi

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.

Keywords:

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Vol. 31, No. 10

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History

Received 26 February 2022

Accepted 28 November 2022

Published: September 29, 2023

Information

This is an Open Access article in the “Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part IV”, edited by Yeliz Karaca https://orcid.org/0000-0001-8725-6719 (University of Massachusetts Chan Medical School, USA), Dumitru Baleanu https://orcid.org/0000-0002-0286-7244 (Cankaya University, Turkey & Institute of Space Sciences, Romania), Majaz Moonis https://orcid.org/0000-0002-9747-0003 (University of Massachusetts Chan Medical School, USA), Yu-Dong Zhang https://orcid.org/0000-0002-4870-1493 (University of Leicester, Leicester, UK) & Osvaldo Gervasi https://orcid.org/0000-0003-4327-520X (Perugia University, Perugia, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND) License which permits use, distribution and reproduction, provided that the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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