A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

BHRAWY A. H. , THARWAT M. M. , Yildirim A.

APPLIED MATHEMATICAL MODELLING, vol.37, no.6, pp.4245-4252, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 6
  • Publication Date: 2013
  • Doi Number: 10.1016/j.apm.2012.08.022
  • Page Numbers: pp.4245-4252
  • Keywords: Multi-term FDEs, Tau method, Shifted Chebyshev polynomials, Chebyshev-Gauss quadrature, Riemann-Liouville sense, BOUNDARY-VALUE-PROBLEMS, OPERATIONAL MATRIX, WAVELET METHOD, COEFFICIENTS, COLLOCATION, EXPANSIONS, SYSTEMS


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.