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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
Applied Mathematical Modelling, Volume 35, No. 12, Year 2011
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Description
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 TL,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. © 2011 Elsevier Inc.
Authors & Co-Authors
Doha, Eid Hassan
Egypt, Giza
Faculty of Science
Bhrawy, Ali H.
Saudi Arabia, Jeddah
King Abdulaziz University
Ezz-Eldien, Samer S.
Egypt, Cairo
Modern Academy
Statistics
Citations: 278
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1016/j.apm.2011.05.011
ISSN:
0307904X