Optimal subalgebras and conservation laws with exact solutions for biological population model

Shagolshem, Sumanta; Bira, B.; Zeidan, Dia

doi:10.1016/j.chaos.2022.112985

Cited by 9 publications

(4 citation statements)

References 20 publications

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“…Recently, it has been argued that the theory of fractional calculus has a wide range of applications and that modeling identical issues using fractional systems yielded more accurate results than modeling them with the ordinary derivatives approach [55] , [56] , [57] , [58] , [59] , [60] , [61] . As a result, we will adapt model (7) to the new framework by using the generalized Mittag-Leffler kernel and fractional derivative:

Under the starting approximation

0000000

…”

Section: Mathematical Modelmentioning

confidence: 99%

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Chu¹,

Zarin²,

Khan³

et al. 2023

Alexandria Engineering Journal

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Under the starting approximation

0000000

…”

Section: Mathematical Modelmentioning

confidence: 99%

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Chu¹,

Zarin²,

Khan³

et al. 2023

Alexandria Engineering Journal

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“…The authors tackled both linear and nonlinear population systems by employing various advanced mathematical techniques, including the variational iteration method, 25 adomain decomposition method, 26 homotopy analysis method, 27 and homotopy perturbation method. 28 Shagolshem et al presented the articles on the one-dimensional blood flow model, 29,30 and a paper on the biological population model with Malthusian law 31 using Lie symmetry analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Shagolshem et al. presented the articles on the one‐dimensional blood flow model, 29,30 and a paper on the biological population model with Malthusian law 31 using Lie symmetry analysis.…”

Section: Introductionmentioning

confidence: 99%

Study of optimal subalgebras, invariant solutions, and conservation laws for a Verhulst biological population model

Sharma,

Arora

2024

Stud Appl Math

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In this research, the (2+1)‐dimensional normal biological population model, incorporating the Verhulst law for population growth, is employed to explore species population dynamics. Employing Lie symmetry analysis, we address a nonlinear degenerate parabolic partial differential equation, yielding much‐improved results. This analysis includes computing one‐dimensional optimal subalgebras, reduced ordinary differential equations, and obtaining invariant solutions with a visual depiction of the physical behavior of the Verhulst biological population model through symmetry group transformations. Additionally, the multiplier method leads to novel conservation laws and potential systems not locally connected to the governing partial differential equation (PDE). These findings have significant implications for understanding and controlling biological populations, offering insights for applications in ecology and the environment.

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“…The 2 + 1 dimensional normal biological population model has been studied using the lie symmetry analysis technique. Also, some conservation laws of the model have been developed there (Shagolshem, 2023). A class of non-linear parabolic partial differential equations with applications in the modelling of oil pollution in water has been solved numerically (Izadi and Zeidan, 2022).…”

Section: Introductionmentioning

confidence: 99%

Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order

Mohapatra

Chakraverty

2023

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PurposeInvestigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.Design/methodology/approachTriangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.FindingsLWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.Originality/valueTo deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

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Optimal subalgebras and conservation laws with exact solutions for biological population model

Cited by 9 publications

References 20 publications

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Study of optimal subalgebras, invariant solutions, and conservation laws for a Verhulst biological population model

Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order

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