title: The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.
abstract: 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.
authors.affiliation: 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.
authors.forename: M M
authors.initials: MM
authors.lastname: Khader
keywords: Caputo fractional derivatives; Laguerre polynomials; error analysis; fractional delay differential equations; spectral collocation method