Dynamical Behaviour of a Caputo Fractional Women Empowerment Model with Control Optimization

Women’s empowerment is a complex socio-economic process that can be influenced by policy interventions; social awareness, culture, memory and hereditary factors play a significant role here. Classical integer-order models do not adequately capture these nonlocal properties. To address this limitation, we propose a Caputo fractional-order [Formula: see text] model to study the dynamics of women’s empowerment using five compartments: [Formula: see text] ordinary class women, [Formula: see text] hurdle-faced women, [Formula: see text] stressed women, [Formula: see text] fear-affected women and [Formula: see text] empowered women. We demonstrated positivity, boundedness, existence and uniqueness of the solutions for well-posedness. To characterize the threshold dynamics, the basic reproduction number [Formula: see text] is derived; the qualitative behaviour of the system is discussed by using local stability, sensitivity analysis and transcritical bifurcation. A Pontryagin’s Maximum Principle-based optimal control problem is formulated and solved numerically using the Forward–Backward Sweep Method. The novelty of this study is the modification of the Caputo [Formula: see text] model, which explicitly represents the intervention effects and incorporates a revised transition mechanism among compartments. The suggested model gives a different description of the obstacles and stress toward empowerment since it takes into account the role of government interventions, unlike the previous formulation. The system obtained is thoroughly explored by equilibrium analysis, stability analysis, sensitivity analysis and transcritical bifurcation analysis. Furthermore, an optimal control framework is developed to determine effective intervention options to reduce difficulties and stress and enhance the empowerment process. Numerical simulations show the effects of the fractional-order memory and the success of various control mechanisms, offering quantitative insights for the formulation of sustainable policies for women’s empowerment.