Bhrawy, A. H.Baleanu, DumitruAssas, L. M.2020-06-022020-06-022014Bhrawy, 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).1077-5463http://hdl.handle.net/20.500.12416/3995The 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.eninfo:eu-repo/semantics/closedAccessTau MethodGeneralized Laguerre-Gauss QuadratureGeneralized Laguerre PolynomialsMulti-Term Fractional Differential EquationsCaputo DerivativeArticle20797398510.1177/1077546313482959