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arXiv · 2406.12856

Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms

Tanzeela Kanwal·Azhar Hussain·İbrahim Avcı·Sina Etemad·Shahram Rezapour·Delfim F. M. Torres
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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.

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Tanzeela Kanwal, Azhar Hussain, İbrahim Avcı, Sina Etemad, Shahram Rezapour, Delfim F. M. Torres. 2024-02-26. Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms. https://doi.org/10.1016/j.chaos.2024.114653

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