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Faculty of Sciences
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 Type
Dr Grade
Email
Eid H Doha
Doha, Eid H
Researcher
Doctorate
eiddoha@frcu.eun.eg
علي حسن بحراوي
Bhrawy, Ali H
Researcher
Doctorate
alibhrawy@yahoo.co.uk
S S Ezz-Eldien
Ezz-Eldien, S S
Researcher
Doctorate
s_sezeldien@yahoo.com
Files
File Name
Type
Description
32628.pdf
pdf
Abstract
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