Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system
The study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adom...
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024164?viewType=HTML |
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| author | D. Priyadarsini P. K. Sahu M. Routaray D. Chalishajar |
| author_facet | D. Priyadarsini P. K. Sahu M. Routaray D. Chalishajar |
| author_sort | D. Priyadarsini |
| collection | DOAJ |
| description | The study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adomain decomposition method (ADM), and the differential transform method (DTM). This study demonstrates the good agreement between the results produced by using the specified computational techniques. The numerical results displayed as graphs demonstrate the accuracy of the computational methods. The approaches that have been established are thus quite relevant and suitable for solving nonlinear fractional models. Meanwhile, the impact of changing the fractional order of a time derivative and time $ t $ on populations of phytoplankton, toxic-phytoplankton, and zooplankton has been examined using graphical representations. Furthermore, the stability analysis of the LTM approach has been discussed. |
| first_indexed | 2024-03-08T12:09:39Z |
| format | Article |
| id | doaj.art-67a272fb864c4cbd9c8a48d7c4f3e346 |
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| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T12:09:39Z |
| publishDate | 2024-01-01 |
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| spelling | doaj.art-67a272fb864c4cbd9c8a48d7c4f3e3462024-01-23T01:35:25ZengAIMS PressAIMS Mathematics2473-69882024-01-01923349336810.3934/math.2024164Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton systemD. Priyadarsini 0P. K. Sahu1M. Routaray 2D. Chalishajar31. Department of Mathematics, School of Applied Sciences, KIIT University, Odisha-751024, India2. Department of Mathematics, Model Degree College, Nayagarh, Odisha-752079, India1. Department of Mathematics, School of Applied Sciences, KIIT University, Odisha-751024, India3. Department of Applied Mathematics, Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450, USAThe study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adomain decomposition method (ADM), and the differential transform method (DTM). This study demonstrates the good agreement between the results produced by using the specified computational techniques. The numerical results displayed as graphs demonstrate the accuracy of the computational methods. The approaches that have been established are thus quite relevant and suitable for solving nonlinear fractional models. Meanwhile, the impact of changing the fractional order of a time derivative and time $ t $ on populations of phytoplankton, toxic-phytoplankton, and zooplankton has been examined using graphical representations. Furthermore, the stability analysis of the LTM approach has been discussed.https://aimspress.com/article/doi/10.3934/math.2024164?viewType=HTMLphytoplankton-toxic phytoplankton-zooplankton systemstability conditionslaplace transform methodadomian decomposition methoddifferential transform method |
| spellingShingle | D. Priyadarsini P. K. Sahu M. Routaray D. Chalishajar Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system AIMS Mathematics phytoplankton-toxic phytoplankton-zooplankton system stability conditions laplace transform method adomian decomposition method differential transform method |
| title | Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system |
| title_full | Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system |
| title_fullStr | Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system |
| title_full_unstemmed | Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system |
| title_short | Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system |
| title_sort | numerical treatment for time fractional order phytoplankton toxic phytoplankton zooplankton system |
| topic | phytoplankton-toxic phytoplankton-zooplankton system stability conditions laplace transform method adomian decomposition method differential transform method |
| url | https://aimspress.com/article/doi/10.3934/math.2024164?viewType=HTML |
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