Fractional Dynamical System for Pollution in Multi-Pond Networks

Aquatic pollution threatens biodiversity, disrupts ecological balance, and poses risks to communities dependent on freshwater resources. Aquaculture ponds are especially susceptible, as contaminants directly influence both ecosystem stability and the safety of fish for human consumption. With the rapid growth of pond-based aquaculture, accurate modeling of pollutant dynamics is essential. This study analyzes pollution in a system of n interconnected ponds, assuming a clean water source, constant volume, and steady pollutant inflow and outflow. A previous model based on ordinary differential equations is solved using matrices, eigenvalues, eigenvectors, and generalized eigenvectors. A generalized fractional model is then developed employing the Caputo–Liouville derivative. Unlike classical models, fractional models account for memory effects and anomalous diffusion, providing a more realistic description of pollutant behavior. Analytical solutions are derived to track pollutant variation across ponds, and a comparison of the two formulations is presented. The results enhance understanding of pollution transport in aquaculture systems and offer insights for sustainable water quality management in fish farming.