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.
The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations
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.
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Khader, M. M. (July 18, 2013). "The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations." ASME. J. Comput. Nonlinear Dynam. October 2013; 8(4): 041018. https://doi.org/10.1115/1.4024852
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