Two efficient generalized Laguerre spectral algorithms for fractional initial value problems. (English) Zbl 1291.65240

Summary: We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. We derive the operational matrix of Caputo fractional derivative of the generalized Laguerre polynomials which is applied together with generalized Laguerre tau approximation for implementing a spectral solution of linear multiterm FDEs on semi-infinite interval subject to initial conditions. The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. Through several numerical examples, we confirm the accuracy and performance of the proposed spectral algorithms. Indeed, the methods yield accurate results, and the exact solutions are achieved for some tested problems.


65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34A08 Fractional ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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