1. Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line.
- Author
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Bhrawy, AH, Baleanu, D, and Assas, LM
- Subjects
- *
NUMERICAL solutions to differential equations , *FRACTIONAL calculus , *LAGUERRE polynomials , *LAGUERRE geometry , *CAPUTO fractional derivatives , *APPROXIMATION theory , *MATHEMATICAL models - 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 Li(α)(x) with x∈Λ=(∞) and i denoting the polynomial degree. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
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