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