Two-dimensional time fractional-order biological population model and its analytical solution

AbstractIn this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional orderα.

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An efficient technique for two-dimensional fractional order biological population model

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962320500051 ◽

2020 ◽

Vol 11 (01) ◽

pp. 2050005 ◽

Cited By ~ 11

Author(s):

P. Veeresha ◽

D. G. Prakasha

Keyword(s):

Numerical Simulation ◽

Differential Equations ◽

Fractional Order ◽

Population Model ◽

Decomposition Method ◽

Arbitrary Order ◽

Two Dimensional ◽

Decomposition Scheme ◽

Biological Population ◽

Natural Decomposition

In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful blend of decomposition scheme with natural transform, and three examples are considered to validate and illustrate its efficiency. The nature of FNDM solution has been captured for distinct arbitrary order. In order to illustrate the proficiency and reliability of the considered scheme, the numerical simulation has been presented. The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

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Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽

10.3390/math9020155 ◽

2021 ◽

Vol 9 (2) ◽

pp. 155

Author(s):

Gbenga O. Ojo ◽

Nazim I. Mahmudov

Keyword(s):

Iterative Method ◽

Fractional Order ◽

Population Model ◽

Numerical Solutions ◽

Computational Effort ◽

Spatial Diffusion ◽

Transform Method ◽

Biological Population ◽

The Laplace Transform ◽

New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

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Study on Approximate Solution of Fractional Order Biological Population Model

Archives of Current Research International ◽

10.9734/acri/2018/46155 ◽

2019 ◽

Vol 15 (4) ◽

pp. 1-11

Author(s):

Yunqi Xu ◽

Dianchen Lu

Keyword(s):

Approximate Solution ◽

Fractional Order ◽

Population Model ◽

Biological Population

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Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

International Journal of Biomathematics ◽

10.1142/s1793524516500819 ◽

2016 ◽

Vol 09 (06) ◽

pp. 1650081 ◽

Cited By ~ 11

Author(s):

S. Sarwar ◽

M. A. Zahid ◽

S. Iqbal

Keyword(s):

Fractional Order ◽

Asymptotic Method ◽

Population Model ◽

Approximate Solutions ◽

High Accuracy ◽

Population Models ◽

Mathematical Study ◽

Third Order ◽

Biological Population ◽

Optimal Homotopy Asymptotic Method

In this paper, we study the fractional-order biological population models (FBPMs) with Malthusian, Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method (OHAM) for partial differential equations (PDEs) is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional-order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

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New wave solutions for the fractional-order biological population model, time fractional burgers, Drinfel’d–Sokolov–Wilson and system of shallow water wave equations and their applications

European Journal of Computational Mechanics ◽

10.1080/17797179.2017.1374233 ◽

2017 ◽

Vol 26 (5-6) ◽

pp. 508-524 ◽

Cited By ~ 13

Author(s):

Aly R. Seadawy ◽

Dianchen Lu ◽

Mostafa M. A. Khater

Keyword(s):

Shallow Water ◽

Fractional Order ◽

Water Wave ◽

Population Model ◽

Wave Equations ◽

New Wave ◽

Shallow Water Wave ◽

Wave Solutions ◽

Biological Population ◽

Shallow Water Wave Equations

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On biological population model of fractional order

International Journal of Biomathematics ◽

10.1142/s1793524516500704 ◽

2016 ◽

Vol 09 (05) ◽

pp. 1650070 ◽

Cited By ~ 12

Author(s):

Syed Tauseef Mohyud-Din ◽

Ayyaz Ali ◽

Bandar Bin-Mohsin

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Exact Solutions ◽

Fractional Order ◽

Population Model ◽

Numerical Data ◽

Population Changes ◽

Partial Differential ◽

Biological Population ◽

Fractional Pdes

In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.

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