Modeling and analysis of the polluted lakes system with various fractional approaches. (May 2020) - El-Dessoky Ahmed, M.M.; Altaf Khan, Muhammad
Highlights: A three lakes system with new operator is presented. A fractal-fractional approach is utilized to obtain new results. A novel numerical procedure is shown for the new operator. Graphical results revealed the importance of fractal-fractional for the three lakes systems. Abstract: The purpose of this paper is to investigate the dynamics of the polluted lakes system through fractional derivative approach in the sense of fractal-fractional operator. Initially, we derive the model based on the assumptions and then apply the fractal-fractional operator. The model with fractal-fractional approach in the sense of Atangana–Baleanu derivative is considered. When, choosing the fractal order one we obtain fractional order, and when choosing the fractional order one a fractal system is obtained. Considering both the operators together we present a model with fractal-fractional. We present a novel numerical approach to solve the fractal-fractional system and then present the existence and uniqueness results for the system. We present various graphical results for the fractal and fractional operators and also for the fractal-fractional orders. The graphical results reveals the significance of the new operator to a practical problem in a better way.