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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
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2013
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vol. 11
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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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Numerical solution of fractional differential equations via a Volterra integral equation approach

100%
Esmaeili S., Shamsi M., Dehghan M.
Open Physics
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2013
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vol. 11
|
issue 10
1470-1481
EN
The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.
3
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Variational iteration method - a promising technique for constructing equivalent integral equations of fractional order

100%
Wang Y.-H., Wu G.-C., Baleanu D.
Open Physics
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2013
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vol. 11
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issue 10
1392-1398
EN
The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method’s new role.
4
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Existence and uniqueness of a complex fractional system with delay

100%
Ibrahim R., Jalab H.
Open Physics
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2013
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vol. 11
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issue 10
1528-1535
EN
Chaotic complex systems are utilized to characterize thermal convection of liquid flows and emulate the physics of lasers. This paper deals with the time-delay of a complex fractional-order Liu system. We have examined its chaos, computed numerical solutions and established the existence and uniqueness of those solutions. Ultimately, we have presented some examples.
5
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Linear Dynamic System Identification in the Frequency Domain Using Fractional Derivatives

88%
Janiczek T., Janiczek J.
Metrology and Measurement Systems
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2010
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issue 2
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