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 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.

A collocation method for numerical solutions of fractional-order logistic population model

2016 ◽  
Vol 09 (02) ◽  
pp. 1650031 ◽  
Author(s):  
Şuayip Yüzbaşı
Keyword(s):  
Approximate Solution ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Model Problem ◽  
Error Function ◽  
Approximate Solutions ◽  
Algebraic Equations

In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.

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 Solving Two Dimensional Coupled Burger's Equations and Sine-Gordon Equation Using El-Zaki Transform-Variational Iteration Method

2021 ◽  
Vol 24 (2) ◽  
pp. 41-47
Author(s):  
Marwa H. Al-Tai ◽  
◽  
Ali Al-Fayadh ◽  
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Partial Differential ◽  
Burger's Equations ◽  
Variation Iteration Method

In this paper, the combined form of the Elzaki transform and variation iteration method is implemented efficiently in finding the analytical and numerical solutions of the two-dimensional nonlinear coupled Burger's partial differential equations and sine-Gordon partial differential equation. The obtained solutions were compared to the exact solutions and other existing methods. Illustrative examples show the efficiency and the power of the used method.

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
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