Mathematical Modeling of Societal Challenges: A Fractional Analysis Perspective

The prevalence of societal issues, such as violence that affects women, has skyrocketed worldwide. To create a society where women can reach their full potential, we need to address the violence and other obstacles that stand in their way, requiring a thoughtful and nuanced mathematical modeling approach. In this paper, a mathematical model that represents a societal challenge facing women is constructed. The proposed model is studied using nonlocal and nonsingular kernels. The mathematical analysis of the positivity of solutions and the invariant region is studied. The fixed-point method is used to prove the existence and uniqueness of the model solution. We analyze the stability of the proposed model using the Picard approach and the Hyers–Ulam criteria. Numerical simulations of the proposed model based on Newton polynomial approximation are established. Sensitivity analyses of the most sensitive parameters are conducted, and the results are discussed. The simulations revealed that changing the fractional order l results in complex behavioral changes within the system. Again, we observe a damp oscillatory pattern in some compartments with certain values of l. The results demonstrate that the number of women who receive assistance increases as time progresses. This trend indicates that helping women can be an effective strategy to reduce gender-based violence. Therefore, healthcare policymakers and lawmakers must prioritize the identification of cases of violence against women, provide support to victims, and implement strict regulations to address this issue. In addition, the government can play a crucial role in protecting against violent acts by offering financial assistance.