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

Subject Areas : Numerical Analysis

bijan hasani lichae ^{1 *} , mehran nemati ²

1 - Department of Mathematics, Fouman Branch, Islamic Azad University, Fouman, Iran
2 - Department of Mathematics, roudbar Branch, Islamic Azad University, roudbar, Iran

Received: 2024-12-27 Accepted : 2025-02-07 Published : 2025-01-13

Keywords: Numerical solution, Laplace Adomian decomposition method, System of fractional-order differential equations of the pollution, Caputo fractional derivative,

Abstract :

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, , the amount of the pollution in lake 2, , and the amount of the pollution in lake 3, , at any time . 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.

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