Modeling the Dynamics of Corruption in Police and Judiciary Systems Using Fractional Order Differential Equations and the Laplace-Adomian Transform Method

Abstract

This study develops a model to better understand how corruption spreads within Police and the judiciary, using fractional-order differential equations and the Laplace-Adomian transform method to capture the complex, non-linear nature of corruption. Corruption in these sectors weakens the rule of law, erodes public trust, and stifles socio-economic growth, yet many existing models oversimplify its causes. By considering the memory-dependent nature and delayed effects of interventions, this research offers a more accurate representation of how corruption evolves over time. The findings highlight the importance of early intervention, sustained accountability, and systemic reforms, showing that while short-term policy changes can help, lasting success requires deeper institutional change. External factors like international oversight or whistleblowing can also play a crucial role, though their effectiveness depends on trust in local institutions. This approach provides a more detailed framework for designing targeted anti-corruption strategies within police and judicial systems, offering valuable insights for policymakers and reformers.