Advancing water quality management: A synergistic approach using fractional differential equations and neural networks

Water pollution significantly threatens public health and environmental sustainability, particularly in developing nations. This study introduced an innovative fractional-order mathematical model for analyzing water pollution dynamics, incorporating four distinct compartments to represent the interactions between polluted water sources, susceptible water bodies, contamination processes, and restoration mechanisms. The model used the Atangana-Baleanu fractional derivative in the Caputo sense, offering a more precise representation of memory effects and complex pollutant transport mechanisms. The proposed model underwent rigorous qualitative validation, ensuring the existence and uniqueness of solutions via fixed-point theory, while stability analysis was conducted using the Ulam-Hyers approach. The Adams-Bashforth numerical method was employed to obtain approximate solutions, enabling a more accurate simulation of pollution dynamics. Numerical simulations further highlighted the impact of treatment strategies in reducing contamination levels and restoring water quality. Additionally, artificial neural networks (ANN) were integrated into the framework to enhance predictive capabilities. The dataset used for ANN training was derived from simulated pollution levels based on model parameters calibrated with empirical studies on water contamination dynamics. This combined fractional-ANN methodology established a robust foundation for effective water quality management, aiding in decision-making for pollution control policies and remediation strategies.