Document Details

Document Type : Article In Journal 
Document Title :
Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
 
Subject : Mathematics 
Document Language : English 
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 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. 
ISSN : 0307-904X 
Journal Name : Applied Mathematical Modelling 
Volume : 35 
Issue Number : 12 
Publishing Year : 1432 AH
2011 AD 
Article Type : Article 
Added Date : Monday, March 12, 2012 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
Eid H DohaDoha, Eid HResearcherDoctorateeiddoha@frcu.eun.eg
علي حسن بحراويBhrawy, Ali HResearcherDoctoratealibhrawy@yahoo.co.uk
S S Ezz-EldienEzz-Eldien, S SResearcherDoctorates_sezeldien@yahoo.com

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