Browsing by Author "Kadem, Abdelouahab"

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About the F-N Approximation to Fractional Neutron Transport Equation in Slab Geometry
(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru; Kadem, Abdelouahab
The neutron transport denotes the study of the motions and interactions of neutrons with materials. In given applications we need to know where neutrons are in an apparatus, what direction they are moving, and how fast they are going. In this manuscript the Legendre polynomial approximation method F-N was applied to the one dimensional slab geometry neutron transport equation.
Citation - WoS: 5
The Fractional Linear Systems of Equations Within an Operational Approach
(Asme, 2013) Saadatmandi, Abbas; Kadem, Abdelouahab; Dehghan, Mehdi; Baleanu, Dumitru
Fractional calculus is a rapidly going area from both experimental and theoretical points of view. As a result new methods and techniques should be developed in order to deal with new types of fractional differential equations. In this paper the operational matrix of fractional derivative together with the tau method are used to solve the linear systems of fractional differential equations. The results of this method are shown by solving three illustrative examples. By comparing the obtained results with the analytic solutions and with the ones provided by three standard methods for solving the fractional differential equations we conclude that our method gave comparable results.
Fractional one-dimensional transport equation within spectral method combined with modified adomian decomposition method
(Amer Soc Mechanical Engineers, 2010) Baleanu, Dumitru; Kadem, Abdelouahab
In this paper the Chebyshev polynomials technique combined with the modified Adomian decomposition method were applied to solve analytically the fractional transport equation in one-dimensional plane geometry.
Citation - WoS: 35
Citation - Scopus: 40
Homotopy Perturbation Method for the Coupled Fractional Lotka-Volterra Equations
(Editura Acad Romane, 2011) Kadem, Abdelouahab; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-Volterra equations.
Citation - WoS: 19
Citation - Scopus: 18
On Fractional Coupled Whitham-Broer Equations
(Editura Acad Romane, 2011) Kadem, Abdelouahab; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
Finding the fractional version of a given classical nonlinear equation or to a given system of differential equations is still an open problem in the field of the fractional calculus. In this paper the homotopy perturbation method is used to find an analytical approximate solution for the coupled Whitham-Broer-Kaup equations. The obtained results indicate that the method is efficient and accurate.
Citation - WoS: 8
Citation - Scopus: 11
Solution of a Fractional Transport Equation by Using the Generalized Quadratic Form
(Elsevier Science Bv, 2011) Baleanu, Dumitru; Kadem, Abdelouahab
In this manuscript the one dimensional fractional transport equation in which the prescribed source and angular flux are spatially quadratic is investigated within the generalized quadratic form method. It is reported that the angular flux satisfies Fick's law and the corresponding scalar flux satisfies the fractional generalization of the classic diffusion equation. (C) 2010 Elsevier B.V. All rights reserved.
Citation - WoS: 46
Citation - Scopus: 48
Solutions of the Fractional Davey-Stewartson Equations With Variational Iteration Method
(Editura Acad Romane, 2012) Baleanu, Dumitru; Jafari, Hossain; Kadem, Abdelouahab; Yılmaz, Tuğba; Baleanu, Dumitru; Yilmaz, Tugba; Matematik; Psikoloji
This paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.
Citation - WoS: 23
Citation - Scopus: 25
Spectral Method for Solution of the Fractional Transport Equation
(Pergamon-elsevier Science Ltd, 2010) Luchko, Yury; Baleanu, Dumitru; Kadem, Abdelouahab
In this paper, the Chebyshev polynomials expansion method is applied to find both an analytical solution of the fractional transport equation in the one-dimensional plane geometry and its numerical approximations. The idea of the method is in reducing of the fractional transport equation to a system of the linear fractional differential equations for the unknown coefficients of the Chebyshev polynomials expansion. The obtained system of equations is then solved by using the operational method for the Caputo fractional derivative.
Citation - WoS: 7
Citation - Scopus: 9
Two-Dimensional Transport Equation as Fredholm Integral Equation
(Elsevier Science Bv, 2012) Baleanu, Dumitru; Kadem, Abdelouahab
The transport equation has many applications in various fields of science and engineering. In this paper we shown that we can transform a transport equation in two-dimensional case into a Fredholm integral equation of the second kind with a compact integral operator for the angular flux by using the Sumudu transform. (C) 2011 Elsevier B.V. All rights reserved.
Citation - WoS: 15
Citation - Scopus: 28
Variational Iteration Method for a Fractional-Order Brusselator System
(Hindawi Ltd, 2014) Kadem, Abdelouahab; Baleanu, D.; Jafari, H.
This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.