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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12856 |
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| _version_ | 1866911924866777088 |
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| author | Kanwal, Tanzeela Hussain, Azhar Avcı, İbrahim Etemad, Sina Rezapour, Shahram Torres, Delfim F. M. |
| author_facet | Kanwal, Tanzeela Hussain, Azhar Avcı, İbrahim Etemad, Sina Rezapour, Shahram Torres, Delfim F. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms Kanwal, Tanzeela Hussain, Azhar Avcı, İbrahim Etemad, Sina Rezapour, Shahram Torres, Delfim F. M. Dynamical Systems 34A08, 65P99 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. |
| title | Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms |
| topic | Dynamical Systems 34A08, 65P99 |
| url | https://arxiv.org/abs/2406.12856 |