The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design

Year 2025, Volume: 8 Issue: 1, 1 - 10

Bahar Karaman , Emrah Karaman

https://doi.org/10.33434/cams.1559808

Abstract

The paper presents the mathematical dynamics and numerical simulations for a fractional-order social media addiction (FSMA) model. This addiction structure is replaced by involving the Caputo fractional (CF) derivative to get the FSMA model. In this study, our main goal is to understand how the fractional derivative impresses the dynamics of the model. Thus, the theoretical properties are first examined. Afterward, the stability properties of the mentioned model are discussed. Besides, the fractional backward differentiation formula (FBDF) displays numerical simulations of the model. Observing both theoretical and numerical results, the two equilibrium points' stability is not impacted by the order of fractional derivatives. However, each solution converges more quickly to its stationary state for higher values of the fractional-order derivative. Finally, we would like to say that the acquired numerical results are compatible with our theoretical outcomes.

Keywords

Fractional backward differentiation formula(FBDF), Social media addiction, Stability analysis

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