<p>Social media platforms have become an essential part of daily life, providing the chance of sharing information, forming connections, and finding enjoyment. However, the excessive use of social media sparked concerns about its possible adverse impact on mental health, especially about addiction and depression. To study the relation between social media addiction and depression, we formulate a fractional order social media addiction and depression model by using the Caputo derivative. The basic reproduction number is calculated for the prediction and existence of diseases in the population. The local stability of disease-free and disease-persisting steady states is formulated through Routh-Hurwitz criteria. To check the significance of parameters, we utilize the partial rank correlation coefficient for sensitivity analysis. The existence and uniqueness of the solution of the model are also discussed to evidence the reliability and well-posedness of the model. We also use Ulam’s stability analysis for the global analysis. Different numerical techniques are applied to simulate the results of the model and error analysis. Graphical results show the efficiency of our theoretical approach with the variation of the fractional order derivative.</p>