A qualitative study on the stability and existence of solutions in a fractional-order water pollution model via the predictor–corrector approach

The potential of fractional-order models to faithfully capture memory effects, anomalous diffusion and long-term persistence in the dynamics of water pollution has attracted a lot of interest in environmental science. A fractional-order water pollution model is presented in this work, along with an efficient numerical method known as the predictor-corrector method for the accurate and computational analysis of the differential equations. The approach ensures excellent accuracy while taking into account the complex and nonlinear systems relationship between environmental conditions, microbial degradation, and contaminants in aquatic environments. The asymptotic behavior of the solution is shown by a thorough stability study, which offers information on the long-term dispersion of pollutants. The existence and uniqueness of the solution are systematically verified using fixed-point theorems, which ensure the mathematical operators of the model. Numerical simulations demonstrate the accuracy of the suggested approach's emissions and degradation predictions under realistic environmental conditions and further confirm its reliability. The results of this study provide a strong computational framework for investigating complex dynamics of water pollution and emphasize the importance of fractional-order models in environmental studies. In addressing fundamental environmental issues and promoting sustainable aquatic ecosystem management, this work highlights the transformative potential of fractional-order modeling by fusing theoretical advancements with practical applications.