A General Fractional Pollution Model for Lakes

doi:10.1007/s42967-021-00135-4

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (3): 1105-1130.doi: 10.1007/s42967-021-00135-4

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A General Fractional Pollution Model for Lakes

Babak Shiri¹, Dumitru Baleanu^2,3

1. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, China;
2. Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey;
3. Institute of Space Sciences, Magurele-Bucharest, Romania

收稿日期:2020-11-30 修回日期:2021-03-20 出版日期:2022-09-20 发布日期:2022-07-04
通讯作者: Babak Shiri,E-mail:shiri@tabrizu.ac.ir;Dumitru Baleanu,E-mail:dumitru@cankaya.edu.tr E-mail:shiri@tabrizu.ac.ir;dumitru@cankaya.edu.tr

A General Fractional Pollution Model for Lakes

Babak Shiri¹, Dumitru Baleanu^2,3

1. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, China;
2. Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey;
3. Institute of Space Sciences, Magurele-Bucharest, Romania

Received:2020-11-30 Revised:2021-03-20 Online:2022-09-20 Published:2022-07-04
Contact: Babak Shiri,E-mail:shiri@tabrizu.ac.ir;Dumitru Baleanu,E-mail:dumitru@cankaya.edu.tr E-mail:shiri@tabrizu.ac.ir;dumitru@cankaya.edu.tr

摘要/Abstract

摘要： A model for the amount of pollution in lakes connected with some rivers is introduced. In this model, it is supposed the density of pollution in a lake has memory. The model leads to a system of fractional differential equations. This system is transformed into a system of Volterra integral equations with memory kernels. The existence and regularity of the solutions are investigated. A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution. Validation examples are supported, and some models are simulated and discussed.

关键词: Amount of pollution in lakes, System of ordinary differential equations, System of fractional differential equations, Explicit and implicit methods, Regularity of the solution

Abstract: A model for the amount of pollution in lakes connected with some rivers is introduced. In this model, it is supposed the density of pollution in a lake has memory. The model leads to a system of fractional differential equations. This system is transformed into a system of Volterra integral equations with memory kernels. The existence and regularity of the solutions are investigated. A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution. Validation examples are supported, and some models are simulated and discussed.

Key words: Amount of pollution in lakes, System of ordinary differential equations, System of fractional differential equations, Explicit and implicit methods, Regularity of the solution

中图分类号:

34A08
45D05

Babak Shiri, Dumitru Baleanu. A General Fractional Pollution Model for Lakes[J]. Communications on Applied Mathematics and Computation, 2022, 4(3): 1105-1130.

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A General Fractional Pollution Model for Lakes

A General Fractional Pollution Model for Lakes

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