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Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms
- Source :
- Chaos Solitons Fractals 181 (2024), Art. 114653, 21 pp
- Publication Year :
- 2024
-
Abstract
- We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal-fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray-Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams-Bashforth and Newton polynomials methods. The effect of fractal-fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic.<br />Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Chaos Solitons Fractals' at [https://doi.org/10.1016/j.chaos.2024.114653]
- Subjects :
- Mathematics - Dynamical Systems
34A08, 65P99
Subjects
Details
- Database :
- arXiv
- Journal :
- Chaos Solitons Fractals 181 (2024), Art. 114653, 21 pp
- Publication Type :
- Report
- Accession number :
- edsarx.2406.12856
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.chaos.2024.114653