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Efficient generalized laguerre-spectral methods for solving multi-term fractional differential equations on the half line

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2014

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Sage Publications LTD

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Abstract

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 is an element of Lambda = (0,infinity) and i denoting the polynomial degree.

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Tau Method, Generalized Laguerre-Gauss Quadrature, Generalized Laguerre Polynomials, Multi-Term Fractional Differential Equations, Caputo Derivative

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Citation

Bhrawy, 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).

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Source

Journal Of Vibration And Control

Volume

20

Issue

7

Start Page

973

End Page

985