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Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
- Source :
-
Applied Mathematical Modelling . Dec2011, Vol. 35 Issue 12, p5662-5672. 11p. - Publication Year :
- 2011
-
Abstract
- Abstract: In this paper, we state and prove a new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted Chebyshev polynomials themselves. We develop also a direct solution technique for solving the linear multi-order fractional differential equations (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 shifted Chebyshev polynomials T L,n (x) with x ∈(0, L), L >0 and n is the polynomial degree. We presented a shifted Chebyshev collocation method with shifted Chebyshev–Gauss points used as collocation nodes for solving nonlinear multi-order fractional initial value problems. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0307904X
- Volume :
- 35
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Applied Mathematical Modelling
- Publication Type :
- Academic Journal
- Accession number :
- 63189732
- Full Text :
- https://doi.org/10.1016/j.apm.2011.05.011