scholarly journals On beta-time fractional biological population model with abundant solitary wave structures

2021 ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Armando Ciancio ◽  
Khalid K. Ali ◽  
M.S. Osman ◽  
Carlo Cattani ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Population Model ◽  
Biological Population

scholarly journals New fractional calculus and application to the fractional-order of extended biological population model

2018 ◽  
Vol 36 (3) ◽  
pp. 115-128 ◽  
Author(s):  
Ahmad Neirameh
Keyword(s):  
Solitary Wave ◽  
Fractional Order ◽  
Population Model ◽  
Conformable Fractional Derivative ◽  
Solitary Wave Solutions ◽  
Fractional Partial Differential Equations ◽  
Wave Solutions ◽  
Biological Population ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this study, we propose a new algorithm to find exact solitary wave solutions of nonlinear time- fractional order of extended biological population model. The new algorithm basically illustrates how two powerful algorithms, conformable fractional derivative and the homogeneous balance method can be combined and used to get exact solutions of fractional partial differential equations.

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 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

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.

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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