Fractional-order mathematical modeling and optimal control strategies for women's empowerment initiatives

Women's empowerment is essential for societal development, with government initiatives playing a pivotal role in this process. This study introduces a fractional-order mathematical model capturing the dynamics of women's empowerment, emphasizing the impact of governmental efforts. The population is divided into five compartments, reflecting the transition from initial challenges to full empowerment. An analytical investigation establishes the existence, uniqueness, positivity, and boundedness of the model's solutions. Stability and sensitivity analyses are performed to explore the effects of key parameters on the system's behavior. Additionally, a fractional-order optimal control model is proposed to help policymakers design effective control strategies. Using Pontryagin's Maximum Principle, we derive conditions for optimal control and compare controlled and uncontrolled scenarios to assess the impact of interventions. Simulation results show that integrated strategies, combining government support and policy interventions, accelerate empowerment outcomes. The fractional model captures the complex dynamic nature of empowerment and provides actionable insights for sustainable development.