Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system

D. Priyadarsini; P. K. Sahu; M. Routaray; D. Chalishajar; D. Priyadarsini; P. K. Sahu; M. Routaray; D. Chalishajar

doi:10.3934/math.2024164

AIMS Mathematics

2024, Volume 9, Issue 2: 3349-3368. doi: 10.3934/math.2024164

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Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system

1.
Department of Mathematics, School of Applied Sciences, KIIT University, Odisha-751024, India
2.
Department of Mathematics, Model Degree College, Nayagarh, Odisha-752079, India
3.
Department of Applied Mathematics, Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450, USA

Received: 24 July 2023 Revised: 14 December 2023 Accepted: 19 December 2023 Published: 05 January 2024
MSC : 26A33, 37N30

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.
Citation: D. Priyadarsini, P. K. Sahu, M. Routaray, D. Chalishajar. Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system[J]. AIMS Mathematics, 2024, 9(2): 3349-3368. doi: 10.3934/math.2024164

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Abstract

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.

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