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Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line. (English) Zbl 1348.65060

Summary: The 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 \(x\in\Lambda=(0,\infty)\) and \(i\) denoting the polynomial degree.

MSC:

65D30 Numerical integration
65D32 Numerical quadrature and cubature formulas
26A33 Fractional derivatives and integrals
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