Analysis of a fractional pollution model in a system of three interconnecting lakes

Yasir Nadeem Anjam; Mehmet Yavuz; Mati ur Rahman; Amna Batool; Yasir Nadeem Anjam; Mehmet Yavuz; Mati ur Rahman; Amna Batool

doi:10.3934/biophy.2023014

AIMS Biophysics

2023, Volume 10, Issue 2: 220-240. doi: 10.3934/biophy.2023014

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Analysis of a fractional pollution model in a system of three interconnecting lakes

1.
Department of Applied Sciences, National Textile University, Faisalabad 37610, Pakistan
2.
Department of Mathematics, Environment & Sustainability Institute, College of Engineering, Mathematics & Physical Sciences, University of Exeter-Penryn Campus, TR10, UK
3.
Necmettin Erbakan University, Department of Mathematics and Computer Sciences, Meram Yeniyol, 42090 Meram, Konya, Türkiye
4.
School of Mathematical Science, Shanghai Jiao Tong University, P.R. China
5.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

Received: 10 February 2023 Revised: 18 May 2023 Accepted: 24 May 2023 Published: 31 May 2023

Water pollution is a critical global concern that demands ongoing scrutiny and revision of water resource policies at all levels to safeguard a healthy living environment. In this study, we focus on examining the dynamics of a fractional-order model involving three interconnected lakes, utilizing the Caputo differential operator. The aim is to investigate the issue of lake pollution by analyzing a system of linear equations that represent the interconnecting waterways. To numerically solve the model, we employ two methods: The Laplace transform with the Adomian decomposition method (LADM) and the Homotopy perturbation method (HPM). We compare the obtained numerical solutions from both methods and present the results. The study encompasses three variations of the model: the periodic input model, the exponentially decaying input model, and the linear input model. MATLAB is employed to conduct numerical simulations for the proposed scheme, considering various fractional orders. The numerical results are further supported by informative graphical illustrations. Through simulation, we validate the suitability of the proposed model for addressing the issue at hand. The outcomes of this research contribute to the understanding and management of water pollution, aiding policymakers and researchers in formulating effective strategies for maintaining water quality and protecting our environment.
Citation: Yasir Nadeem Anjam, Mehmet Yavuz, Mati ur Rahman, Amna Batool. Analysis of a fractional pollution model in a system of three interconnecting lakes[J]. AIMS Biophysics, 2023, 10(2): 220-240. doi: 10.3934/biophy.2023014

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Abstract

Water pollution is a critical global concern that demands ongoing scrutiny and revision of water resource policies at all levels to safeguard a healthy living environment. In this study, we focus on examining the dynamics of a fractional-order model involving three interconnected lakes, utilizing the Caputo differential operator. The aim is to investigate the issue of lake pollution by analyzing a system of linear equations that represent the interconnecting waterways. To numerically solve the model, we employ two methods: The Laplace transform with the Adomian decomposition method (LADM) and the Homotopy perturbation method (HPM). We compare the obtained numerical solutions from both methods and present the results. The study encompasses three variations of the model: the periodic input model, the exponentially decaying input model, and the linear input model. MATLAB is employed to conduct numerical simulations for the proposed scheme, considering various fractional orders. The numerical results are further supported by informative graphical illustrations. Through simulation, we validate the suitability of the proposed model for addressing the issue at hand. The outcomes of this research contribute to the understanding and management of water pollution, aiding policymakers and researchers in formulating effective strategies for maintaining water quality and protecting our environment.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Conflict of interest

Mehmet Yavuz is a guest editor for AIMS Biophysics and was not involved in the editorial review or the decision to publish this article. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author's contributions

All the authors contributed equally to the writing of this paper. All authors have read and agreed to the published version of the manuscript.

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