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1
Content available remote

Fractional calculus: theory and numerical methods

100%
Vázquez L., Jafari H.
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2
Content available remote

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

81%
Jafari H., Khalique C., Ramezani M., Tajadodi H.
Open Physics
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2013
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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.
3
Content available remote

The variational iteration method for solving n-th order fuzzy differential equations

81%
Jafari H., Saeidy M., Baleanu D.
Open Physics
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2012
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vol. 10
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issue 1
76-85
EN
The variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.
4
Content available remote

Homotopy analysis method for solving Abel differential equation of fractional order

81%
Jafari H., Sayevand K., Tajadodi H., Baleanu D.
Open Physics
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2013
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vol. 11
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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.
5
Content available remote

On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

71%
Babolian E., Hamedzadeh D., Jafari H., Hajikandi A. A., Baleanu D.
Open Physics
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2015
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vol. 13
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issue 1
EN
This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x0, y0) is used. The integrals that appear in this method are computed exactly and some of these integrals are computed with the Cauchy principal value without using numerical quadratures. The solution in the Legendre polynomial form generates a system of linear algebraic equations, this system is solved numerically. Through numerical examples, performance of the present method is discussed concerning the accuracy of the method.
6
Content available remote

Fractional sub-equation method for the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation

61%
Jafari H., Tajadodi H., Baleanu D., Al-Zahrani A., Alhamed Y., Zahid A.
Open Physics
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2013
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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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