ORIGINAL PAPER

A General Fractional Pollution Model for Lakes

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  • 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 date: 2020-11-30

  Revised date: 2021-03-20

  Online published: 2022-07-04

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.

Cite this article

Babak Shiri, Dumitru Baleanu . A General Fractional Pollution Model for Lakes[J]. Communications on Applied Mathematics and Computation, 2022 , 4(3) : 1105 -1130 . DOI: 10.1007/s42967-021-00135-4

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