A novel approach for fractional model of water pollution management

Abstract

Water contamination has been found to have significant detrimental impacts on both the natural environment and human populations. Throughout history, lakes have played a pivotal role in sustaining life, fostering civilizations, and driving economic activities, owing to the indispensable nature of water. Researchers employ a range of mathematical models to facilitate strategic planning for pollution management and environmental preservation. This paper introduces a novel fractional model for the purpose of addressing water pollution in a system of interconnected lakes. The suggested model incorporates the Caputo differential operator, and a highly effective numerical approach is developed for solving this model. This study investigates contamination levels in three distinct scenarios within each lake: impulse imposed pollutant source, exponentially decaying imposed pollutant source, and periodic imposed pollutant source. The convergence and error analysis of the proposed approach are performed, and the main results indicate that the solutions are more accurate, stable, and efficient when compared to the existing benchmark in the literature. Using this model, a realistic approach is put forward to manage lake pollution, taking into account not only flow rates and volumes but also memory effect. Moreover, this research has the potential to enhance comprehension and mitigation strategies associated with water management.