scholarly journals New exact solution of generalized biological population model

2017 ◽  
Vol 10 (07) ◽  
pp. 3916-3929 ◽  
Author(s):  
Omer Acan ◽  
Maysaa Mohamed Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solution ◽  
Population Model ◽  
Biological Population

scholarly journals Exact solution to non-linear biological population model with fractional order

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 317-327 ◽  
Author(s):  
Samia Bushnaq ◽  
Sajjad Ali ◽  
Kamal Shah ◽  
Muhammad Arif
Keyword(s):  
Exact Solution ◽  
Asymptotic Method ◽  
Population Model ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Convergent Series ◽  
New Approach ◽  
Biological Population ◽  
Fractional Models ◽  
Optimal Homotopy Asymptotic Method

In this paper, optimal homotopy asymptotic method has been extended to seek out the exact solution of fractional generalized biological population models. The time fractional derivatives are described in the Caputo sense. It optimal homotopy asymptotic method is a new approach for fractional models. The proposed approach presents a procedure by that we have transferred the model to a series of simpler problems which are solvable by hand work applying the Riemann-Liouville fractional integral operator and obtained exact solution of fractional the generalized biological population by adding the solutions of first three simple problems of the series of simpler problems. The new approach provides exact solution in the way of smoothly convergent series.

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.

Exact Solution of Semi-linear Fuzzy System

2017 ◽  
Vol 84 (3-4) ◽  
pp. 225
Author(s):  
Purnima K. Pandit
Keyword(s):  
Dynamical System ◽  
Exact Solution ◽  
Fuzzy System ◽  
Population Model ◽  
Real Life ◽  
Initial Condition ◽  
Linear Dynamical System

In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.

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