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Numerical solution of fractional differential equations by using fractional B-spline

100%
Jafari H., Khalique C., Ramezani M., Tajadodi H.
Open Physics
|
2013
|
vol. 11
|
issue 10
1372-1376
EN
In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.
2
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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.
3
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Fractional sub-equation method for the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation

76%
Jafari H., Tajadodi H., Baleanu D., Al-Zahrani A., Alhamed Y., Zahid A.
Open Physics
|
2013
|
vol. 11
|
issue 10
1482-1486
EN
In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is described in the Jumarie’s modified Riemann-Liouville sense. Two illustrative examples are given, showing the accuracy and convenience of the method.
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