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Travelling wave solutions: A new approach to the analysis of nonlinear physical phenomena

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Sayevand K., Baleanu D., Fardi M.
Open Physics
|
2014
|
vol. 12
|
issue 7
480-489
EN
In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.
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Homotopy analysis method for solving Abel differential equation of fractional order

100%
Jafari H., Sayevand K., Tajadodi H., Baleanu D.
Open Physics
|
2013
|
vol. 11
|
issue 10
1523-1527
EN
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.
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