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.

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 On local fractional operators View of computational complexity: Diffusion and relaxation defined on cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 755-767 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Zhi-Zhen Zhang ◽  
Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Computational Complexity ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Systems ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Cantor Sets ◽  
Fractional Operators ◽  
Fractional Partial Differential Equations ◽  
Comparative Results

This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.

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.

scholarly journals Solving Singular Boundary Value Problems by Optimal Homotopy Asymptotic Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
S. Zuhra ◽  
S. Islam ◽  
M. Idrees ◽  
Rashid Nawaz ◽  
I. A. Shah ◽  
...  
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Boundary Value ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Optimal Homotopy Asymptotic Method

In this paper, optimal homotopy asymptotic method (OHAM) for the semianalytic solutions of nonlinear singular two-point boundary value problems has been applied to several problems. The solutions obtained by OHAM have been compared with the solutions of another method named as modified adomain decomposition (MADM). For testing the success of OHAM, both of the techniques have been analyzed against the exact solutions in all problems. It is proved by this paper that solutions of OHAM converge rapidly to the exact solution and show most effectiveness as compared to MADM.

scholarly journals On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
A. K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Exact Solutions ◽  
Asymptotic Method ◽  
Arbitrary Order ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Optimal Homotopy Asymptotic Method ◽  
Reliable Methods

Two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), are presented. Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. The approximate solutions thus obtained for the fractional Burgers-Fisher and generalized Fisher equations are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparison between the obtained solutions with the exact solutions exhibits that both the featured methods are effective and efficient in solving nonlinear problems. The obtained results justify the applicability of the proposed methods for fractional order Burgers-Fisher and generalized Fisher’s equations.

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.

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