Browsing by Author "Assas, L. M."

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Citation Count: Bhrawy, AH.; Baleanu, Dumitru; Assas, LM., "Efficient generalized laguerre-spectral methods for solving multi-term fractional differential equations on the half line" Journal Of Vibration And Control, Vol.20, No.7, pp.973-985, (2014).
Efficient generalized laguerre-spectral methods for solving multi-term fractional differential equations on the half line
(Sage Publications LTD, 2014) Bhrawy, A. H.; Baleanu, Dumitru; Assas, L. M.; 56389
The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) on the half line with constant coefficients using a generalized Laguerre tau (GLT) method. The fractional derivatives are described in the Caputo sense. We state and prove a new formula expressing explicitly the derivatives of generalized Laguerre polynomials of any degree and for any fractional order in terms of generalized Laguerre polynomials themselves. We develop also a direct solution technique for solving the linear multi-order FDEs with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives described in the Caputo sense are based on generalized Laguerre polynomials L-i((alpha))(x) with x is an element of Lambda = (0,infinity) and i denoting the polynomial degree.
Citation Count: Bhrawy, A. H...et al. (2013). "On a Generalized Laguerre Operational Matrix of Fractional Integration", Mathematical Problems In Engineering.
On A Generalized Laguerre Operational Matrix of Fractional Integration
(Hindawi LTD, 2013) Bhrawy, A. H.; Baleanu, Dumitru; Assas, L. M.; Tenreiro Machado, J. A.; 56389
A new operational matrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with generalized Laguerre tau method for solving general linear multiterm fractional differential equations (FDEs). The method has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposed method is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.