The fractional-order differential model of the pollution for a system of lakes

Pollution produced by human is a serious danger to the planet Earth in our time. In recent decades, a lot of efforts have been made to monitor and control the pollution to save the environment. In this paper, the fractional-order differential model of the pollution for a system of lakes has been introduced. There are three components; the amount of the pollution in lake 1, x , the amount of the pollution in lake 2, y , and the amount of the pollution in lake 3, z , at any time t ≥0 . The aim of this work is to get numerical solution of the proposed fractional-order model by Laplace Adomian decomposition method (LADM). The numerical solution has been obtained in a series form. The solution has been compared with the solutions of some other numerical approaches. The results illustrate the ability and accuracy of the present method . The Caputo form has been applied for fractional derivatives. All of computations have been done in Maple.