Fractional modeling for prey and predator problem by using optimal homotopy asymptotic method

2020 ◽  
Vol 9 (2) ◽  
pp. 35
Author(s):  
Jafar Biazar ◽  
Saghi Safaei ◽  
Martin Tango
Keyword(s):  
Approximate Solution ◽  
Asymptotic Method ◽  
Population Model ◽  
Fractional Derivatives ◽  
Predator Population ◽  
Fractional Modeling ◽  
Optimal Homotopy Asymptotic Method

In this paper, a fractional-ordered prey and predator population model is introduced and applied to obtain an approximate solution with help of optimal homotopy asymptotic method (OHAM). Some plots for populations of the prey and the predator versus time are presented to show the efficiency and the accuracy of the method and confirm that the method is straightforward as well. The fractional derivatives are described in the Caputo sense. 

scholarly journals Applications of OHAM and MOHAM for Fractional Seventh-Order SKI Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jafar Biazar ◽  
Saghi Safaei
Keyword(s):  
Approximate Solution ◽  
Comparative Study ◽  
Exact Solutions ◽  
Asymptotic Method ◽  
Fractional Derivatives ◽  
Fractional Partial Differential Equations ◽  
Large Interval ◽  
Seventh Order ◽  
Optimal Homotopy Asymptotic Method ◽  
Ito Equation

In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

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 Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. K. Alomari ◽  
N. Ratib Anakira ◽  
A. Sami Bataineh ◽  
I. Hashim
Keyword(s):  
Fluid Flow ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Series Solution ◽  
Flow Problem ◽  
Point Boundary ◽  
Optimal Homotopy Asymptotic Method ◽  
First Time

We extend for the first time the applicability of the Optimal Homotopy Asymptotic Method (OHAM) to find approximate solution of a system of two-point boundary-value problems (BVPs). The OHAM provides us with a very simple way to control and adjust the convergence of the series solution using the auxiliary constants which are optimally determined. Comparisons made show the effectiveness and reliability of the method.

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.

scholarly journals Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1530
Author(s):  
Remus-Daniel Ene ◽  
Camelia Pop ◽  
Camelia Petrişor
Keyword(s):  
Systematic Review ◽  
Approximate Solution ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Analytical Integration ◽  
Optimal Homotopy Asymptotic Method ◽  
Special Case

The main goal of this paper is to present an analytical integration in connection with the geometrical frame given by the Hamilton–Poisson formulation of a specific case of Chen’s system. In this special case we construct an analytic approximate solution using the Multistage Optimal Homotopy Asymptotic Method (MOHAM). Numerical simulations are also presented in order to make a comparison between the analytic approximate solution and the corresponding numerical solution.

scholarly journals Optimal Homotopy Asymptotic Method to Nonlinear Damped Generalized Regularized Long-Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
R. Nawaz ◽  
S. Islam ◽  
I. A. Shah ◽  
M. Idrees ◽  
H. Ullah
Keyword(s):  
Wave Equation ◽  
Approximate Solution ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Optimal Homotopy Asymptotic Method ◽  
2D Images

A new semianalytical technique optimal homology asymptotic method (OHAM) is introduced for deriving approximate solution of the homogeneous and nonhomogeneous nonlinear Damped Generalized Regularized Long-Wave (DGRLW) equation. We tested numerical examples designed to confine the features of the proposed scheme. We drew 3D and 2D images of the DGRLW equations and the results are compared with that of variational iteration method (VIM). Results reveal that OHAM is operative and very easy to use.

scholarly journals An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hakeem Ullah ◽  
Saeed Islam ◽  
Muhammad Idrees ◽  
Mehreen Fiza ◽  
Zahoor Ul Haq
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method

We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

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