A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations
Articles > Article ยท 2013
Authors: A. H. BHRAWY, M. M. THARWAT, Ahmet YILDIRIM
APPLIED MATHEMATICAL MODELLING, Journal Indexed in SCI Expanded, International, 2013, vol 37, pp 4245-4252
DOI: 10.1016/j.apm.2012.08.022
Summary
A new explicit formula for the integrals of shifted Chebyshev polynomials of any degree for any fractional-order in terms of shifted Chebyshev polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of linear multi-order fractional differential equations (FDEs) by considering their integrated forms. The shifted Chebyshev spectral tau (SCT) method based on the integrals of shifted Chebyshev polynomials is applied to construct the numerical solution for such problems. The method is then tested on examples. It is shown that the SCT yields better results. (C) 2012 Elsevier Inc. All rights reserved.