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A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations |
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| Authors: | AH Bhrawy MM Tharwat A Yildirim |
| Institution: | 1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA |
| Abstract: | 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. |
| Keywords: | Multi-term FDEs Tau method Shifted Chebyshev polynomials Chebyshev&ndash Gauss quadrature Riemann&ndash Liouville sense |
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