Mathematical Modeling of Divorce Incidence With Social Media Influence Using Caputo Fractional Derivative

Divorce has been an issue of concern in recent years, and with the emergence of social media, these issues are getting out of hand. Social media is seen to contribute to marital conflict by facilitating infidelity and promoting unrealistic expectations from couples, among other things. As a result, this study examines the impact of social media on divorce using the Caputo fractional derivative. The existence and uniqueness of our solution were proven using Banach fixed point theory. Moreover, we calculated the reproduction number and equilibrium points. Our model was then solved and simulated using the generalized Adams–Bashforth–Moulton method. According to our findings, social media plays a significant role in escalating divorce rates through the interactions couples have with divorced people. Again, we found out that social media increases relationship pressures and stresses as well as amplifies misunderstandings between partners, leading to increased tension and conflict. We therefore recommend the need for couples to establish boundaries around social media usage to mitigate its negative effects on their relationship. Our study highlights the importance of thinking about digital communication in modern relationships, as well as the potential benefits of incorporating social media awareness into therapeutic interventions.