Fractional-order modeling and optimal control of corruption dynamics in Police and Judiciary Systems

This study explores corruption dynamics in police and judiciary systems using Fractional Order Differential Equations (FODEs), which capture memory and hereditary effects, offering deeper insight into corruption progression. Integrating Optimal Control Theory, the research designs feasible intervention strategies under real-world constraints. An FODE-based model is developed, and numerical simulations, combined with sensitivity analysis, identify parameters most influencing corruption, guiding targeted interventions. Optimized strategies, including public sensitization, education campaigns, and punitive measures against corrupt officials, are assessed for effectiveness. Results show that combining these interventions substantially reduces corruption compared to uncontrolled scenarios. The study emphasizes multi-pronged, tailored strategies and demonstrates the value of fractional-order modeling for understanding complex socio-institutional phenomena. Findings provide actionable guidance for policymakers to implement effective anti-corruption measures and establish a foundation for future research aimed at refining and extending these strategies for more adaptive and evidence-based governance frameworks.