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

2020 ◽  
Vol 11 (01) ◽  
pp. 2050005 ◽  
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.

scholarly journals Numerical solution of two dimensional time fractional-order biological population model

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 177-186 ◽  
Author(s):  
Amit Prakash ◽  
Manoj Kumar
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Iteration Method ◽  
Population Model ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Spatial Diffusion ◽  
Two Dimensional ◽  
Degenerate Problem ◽  
Biological Population

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.

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

2014 ◽  
Vol 1 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Vineet K. Srivastava ◽  
Sunil Kumar ◽  
Mukesh K. Awasthi ◽  
Brajesh Kumar Singh
Keyword(s):  
Analytical Solution ◽  
Fractional Order ◽  
Population Model ◽  
Two Dimensional ◽  
Biological Population

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

Mathematics ◽  
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.

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

HE–ELZAKI METHOD FOR SPATIAL DIFFUSION OF BIOLOGICAL POPULATION

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950069 ◽  
Author(s):  
JAMSHAID UL RAHMAN ◽  
DIANCHEN LU ◽  
MUHAMMAD SULEMAN ◽  
JI-HUAN HE ◽  
MUHAMMAD RAMZAN
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Population Model ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Numerical Procedure ◽  
Spatial Diffusion ◽  
Homotopy Perturbation ◽  
Biological Population

The foremost purpose of this paper is to present a valuable numerical procedure constructed on Elzaki transform and He’s Homotopy perturbation method (HPM) for nonlinear partial differential equation arising in spatial flow characterizing the general biological population model for animals. The actions are made usually by mature animals driven out by intruders or by young animals just accomplished maturity moving out of their parental region to initiate breeding region of their own. He–Elzaki method is a blend of Elzaki transform and He’s HPM. The results attained are compared with Sumudu decomposition method (SDM). The numerical results attained by suggested method specify that the procedure is easy to implement and precise. These outcomes reveal that the proposed method is computationally very striking.

scholarly journals Systems of nonlinear Volterra integro-differential equations of arbitrary order

2018 ◽  
Vol 36 (4) ◽  
pp. 33-54 ◽  
Author(s):  
Kourosh Parand ◽  
Mehdi Delkhosh
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Approximate Method ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Arbitrary Order ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Arbitrary Integer ◽  
Orthogonal Functions

In this paper, a new approximate method for solving of systems of nonlinear Volterra integro-differential equations of arbitrary (integer and fractional) order is introduced. For this purpose, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) based on the classical Chebyshev polynomials of the first kind has been introduced that can be used to obtain the solution of the integro-differential equations (IDEs). Also, we construct the fractional derivative operational matrix of order $\alpha$ in the Caputo's definition for GFCFs. This method reduced a system of IDEs by collocation method into a system of algebraic equations. Some examples to illustrate the simplicity and the effectiveness of the propose method have been presented.

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

2016 ◽  
Vol 09 (06) ◽  
pp. 1650081 ◽  
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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