Solution of fractional-order integro-differential equations using optimal homotopy asymptotic method

2020 ◽  
Author(s):  
Rashid Nawaz ◽  
Abraiz Khattak ◽  
Muhammad Akbar ◽  
Sumbal Ahsan ◽  
Zahir Shah ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Asymptotic Method ◽  
Optimal Homotopy Asymptotic 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 Extension of Optimal Homotopy Asymptotic Method with Use of Daftardar–Jeffery Polynomials to Coupled Nonlinear-Korteweg-De-Vries System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Rashid Nawaz ◽  
Zawar Hussain ◽  
Abraiz Khattak ◽  
Adam Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Asymptotic Method ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Higher Order ◽  
Partial Differential ◽  
De Vries ◽  
Optimal Homotopy Asymptotic Method

In this paper, Daftardar–Jeffery Polynomials are introduced in the Optimal Homotopy Asymptotic Method for solution of a coupled system of nonlinear partial differential equations. The coupled nonlinear KdV system is taken as test example. The results obtained by the proposed method are compared with the multistage Optimal Homotopy Asymptotic Method. The results show the efficiency and consistency of the proposed method over the Optimal Homotopy Asymptotic Method. In addition, accuracy of the proposed method can be improved by taking higher order approximations.

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