scholarly journals Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order

2013 ◽  
Vol 52 (4) ◽  
pp. 807-812 ◽  
Author(s):  
K. Sayevand ◽  
M. Fardi ◽  
E. Moradi ◽  
F. Hemati Boroujeni
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

scholarly journals Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.

scholarly journals Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Shumaila Javeed ◽  
Dumitru Baleanu ◽  
Asif Waheed ◽  
Mansoor Shaukat Khan ◽  
Hira Affan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation ◽  
The Given ◽  
Ordinary Derivative

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

Solving linear fractional-order differential equations via the enhanced homotopy perturbation method

2009 ◽  
Vol T136 ◽  
pp. 014035 ◽  
Author(s):  
E Naseri ◽  
R Ghaderi ◽  
A Ranjbar N ◽  
J Sadati ◽  
M Mahmoudian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation

scholarly journals Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations

2014 ◽  
Vol 11 (4) ◽  
pp. 1637-1648
Author(s):  
Baghdad Science Journal
Keyword(s):  
Theoretical Analysis ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Infinite Series ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Powerful Method ◽  
Homotopy Perturbation ◽  
Fractional Order Integral

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

ANALYTICAL COMPARISON BETWEEN THE HOMOTOPY PERTURBATION METHOD AND VARIATIONAL ITERATION METHOD FOR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

2008 ◽  
Vol 22 (23) ◽  
pp. 4041-4058 ◽  
Author(s):  
ZAID ODIBAT ◽  
SHAHER MOMANI
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Different Types

Comparison of homotopy perturbation method (HPM) and variational iteration method (VIM) is made, revealing that the two methods can be used as alternative and equivalent methods for obtaining analytic and approximate solutions for different types of differential equations of fractional order. Furthermore, the former is more general and powerful than the latter. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.

scholarly journals Approximate Solution of Multi-Term Fractional Order Delay Differential Equations Using Homotopy Perturbation Method

2020 ◽  
Vol 23 (2) ◽  
pp. 60-66
Author(s):  
Mohammed S. Ismael ◽  
◽  
Fadhel S. Fadhel ◽  
Ali Al-Fayadh ◽  
◽  
...  
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Delay Differential
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