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Research Papers

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

[+] Author and Article Information
M. M. Khader

Department of Mathematics and Statistics,
College of Science,
Al-Imam Mohammed Ibn Saud,
Islamic University (IMSIU),
Riyadh 11566, Saudi Arabia
e-mail: mohamedmbd@yahoo.com

1Permanent address: Department of Mathematics, Faculty of Science, Benha University, Benha, 13518 Egypt.

Contributed by Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received August 23, 2012; final manuscript received April 2, 2013; published online July 18, 2013. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(4), 041018 (Jul 18, 2013) (5 pages) Paper No: CND-12-1130; doi: 10.1115/1.4024852 History: Received August 23, 2012; Revised April 02, 2013

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

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Figures

Grahic Jump Location
Fig. 1

The behavior of the exact solution and the approximate solution at m = 3 and m = 5

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