Enhancing Water Pollution Management Through a Comprehensive Fractional Modeling Framework and Optimal Control Techniques

Abstract Water pollution poses a significant threat to public health, particularly in developing nations. This study aims to enhance our understanding of water pollution transmission dynamics by introducing a novel mathematical model within a general fractional framework. The model offers a comprehensive analysis, including assessing solution feasibility and the stability of equilibrium points. To effectively implement this model, we develop an efficient numerical scheme based on the trapezoidal method. Furthermore, we conduct a thorough error discussion and convergence analysis. Notably, we devise and evaluate a new strategy to effectively tackle the associated fractional optimal control problem concerning water pollutant transmission. Applying this approach to a real case demonstrates its substantial impact, notably in reducing non-soluble contaminants within the water transmission system.