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

IF 1.1 Q4 BIOPHYSICS
Y. N. Anjam, Mehmet Yavuz, Mati ur Rahman, Amna Batool
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引用次数: 2

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.
三个相连湖泊系统的分级污染模型分析
水污染是全球关注的一个重大问题,要求各级不断审查和修订水资源政策,以保障健康的生活环境。在这项研究中,我们重点研究了涉及三个相互关联的湖泊的分数阶模型的动力学,利用卡普托微分算子。目的是通过分析代表相互连接的水道的线性方程组来调查湖泊污染问题。本文采用拉普拉斯变换与Adomian分解法(LADM)和同伦摄动法(HPM)两种方法对模型进行数值求解。我们比较了两种方法得到的数值解,并给出了结果。该研究包含了模型的三种变体:周期输入模型、指数衰减输入模型和线性输入模型。利用MATLAB对所提出的方案进行了数值模拟,考虑了不同分数阶的情况。数值结果进一步得到了信息丰富的图形插图的支持。通过仿真,我们验证了所提出的模型对解决手头问题的适用性。本研究结果有助于了解和管理水污染,帮助决策者和研究人员制定有效的策略来维持水质和保护我们的环境。
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来源期刊
AIMS Biophysics
AIMS Biophysics BIOPHYSICS-
CiteScore
2.40
自引率
20.00%
发文量
16
审稿时长
8 weeks
期刊介绍: AIMS Biophysics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in the field of biophysics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports. AIMS Biophysics welcomes, but not limited to, the papers from the following topics: · Structural biology · Biophysical technology · Bioenergetics · Membrane biophysics · Cellular Biophysics · Electrophysiology · Neuro-Biophysics · Biomechanics · Systems biology
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