Simulations and control for chemical components interaction in environment with generalized fractal fractional operator water pollutants model

Abstract

In this paper, we developed a mathematical model for water pollution dynamics using the fractal fractional operator in the context of the Mittag-Leffler function. Water contamination poses a significant threat to community health, particularly in developing countries. The fractional framework enables a more accurate representation of memory effects and non-local interactions in pollutant dispersion. We will provide fundamental characteristics of the model, such as positivity, boundedness, and the presence of a single solution, with advanced analysis. We establish the existence and uniqueness of solutions to the model using fixed-point theorems, ensuring the mathematical accuracy of the approach. Stability analysis is examined through Ulam-Hyers analysis, and chaos stability is investigated to assess robustness. For numerical approximation, the Newton polynomial method is applied, demonstrating improved computational efficiency and convergence. Numerical simulations confirm that solutions converge more rapidly to a steady state as the fractional order decreases, validating the applicability of the proposed scheme. These results provide a rigorous mathematical foundation and efficient computational framework for analyzing pollutant dynamics, offering valuable insights for environmental modeling and control strategies.