Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

2021 ◽  
Author(s):  
Saima Rashid ◽  
Khadija Tul Kubra Lehre ◽  
Sana Ullah Lehre
Keyword(s):  
Population Model ◽  
Integral Transform ◽  
Spatial Diffusion ◽  
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.

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 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 A Reliable Computational Algorithm for Solving Fractional Biological Population Model

2021 ◽  
Vol 13 (1) ◽  
pp. 59-71
Author(s):  
A. Devi ◽  
M. Jakhar
Keyword(s):  
Perturbation Method ◽  
Population Model ◽  
Homotopy Perturbation Method ◽  
Computational Algorithm ◽  
Spatial Diffusion ◽  
Fractional Partial Differential Equations ◽  
Homotopy Perturbation ◽  
Biological Population ◽  
Fractional Orders ◽  
Real World Problems

In this work, authors obtained the series solution of nonlinear fractional partial differential equations, which is emerging in a spatial diffusion of biological population model using Elzaki transform homotopy perturbation method (ETHPM). The Elzaki transform homotopy perturbation method is a combined form of the Elzaki transform and homotopy perturbation method. Three test illustrations are used to show the proficiency and accuracy of the projected method. It has been observed that the proposed technique can be widely employed to examine other real world problems. The results obtained with the help of the proposed technique are plotted for different fractional orders.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals A novel approach for numeric study of 2D biological population model

2016 ◽  
Vol 3 (1) ◽  
pp. 1261527 ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Vladimir Evgenyevich Fedorov
Keyword(s):  
Population Model ◽  
Biological Population ◽  
Novel Approach
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