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Dynamical Analysis of Two-Dimensional Fractional-Order-in-Time Biological Population Model Using Chebyshev Spectral Method

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Název: Dynamical Analysis of Two-Dimensional Fractional-Order-in-Time Biological Population Model Using Chebyshev Spectral Method
Autoři: Ishtiaq Ali
Zdroj: Fractal and Fractional, Vol 8, Iss 6, p 325 (2024)
Informace o vydavateli: MDPI AG
Rok vydání: 2024
Sbírka: Directory of Open Access Journals: DOAJ Articles
Témata: fractional-order-in-time biological population model, Chebyshev spectral method, error analysis, numerical examples, Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433
Popis: In this study, we investigate the application of fractional calculus to the mathematical modeling of biological systems, focusing on fractional-order-in-time partial differential equations (FTPDEs). Fractional derivatives, especially those defined in the Caputo sense, provide a useful tool for modeling memory and hereditary characteristics, which are problems that are frequently faced with integer-order models. We use the Chebyshev spectral approach for spatial derivatives, which is known for its faster convergence rate, in conjunction with the L 1 scheme for time-fractional derivatives because of its high accuracy and robustness in handling nonlocal effects. A detailed theoretical analysis, followed by a number of numerical experiments, is performed to confirmed the theoretical justification. Our simulation results show that our numerical technique significantly improves the convergence rates, effectively tackles computing difficulties, and provides a realistic simulation of biological population dynamics.
Druh dokumentu: article in journal/newspaper
Jazyk: English
Relation: https://www.mdpi.com/2504-3110/8/6/325; https://doaj.org/toc/2504-3110; https://doaj.org/article/4000d2aac90346358bd70ec124ff736d
DOI: 10.3390/fractalfract8060325
Dostupnost: https://doi.org/10.3390/fractalfract8060325
https://doaj.org/article/4000d2aac90346358bd70ec124ff736d
Přístupové číslo: edsbas.3D5E0A4A
Databáze: BASE
Popis
Abstrakt:In this study, we investigate the application of fractional calculus to the mathematical modeling of biological systems, focusing on fractional-order-in-time partial differential equations (FTPDEs). Fractional derivatives, especially those defined in the Caputo sense, provide a useful tool for modeling memory and hereditary characteristics, which are problems that are frequently faced with integer-order models. We use the Chebyshev spectral approach for spatial derivatives, which is known for its faster convergence rate, in conjunction with the <semantics> L 1 </semantics> scheme for time-fractional derivatives because of its high accuracy and robustness in handling nonlocal effects. A detailed theoretical analysis, followed by a number of numerical experiments, is performed to confirmed the theoretical justification. Our simulation results show that our numerical technique significantly improves the convergence rates, effectively tackles computing difficulties, and provides a realistic simulation of biological population dynamics.
DOI:10.3390/fractalfract8060325