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

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Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, background): “Bhrawy et al. (2013) derived 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.”
Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations (2013, methodology): “Following this method, operational matrix of fractional derivative should be determined for some type of orthogonal polynomials such as Chebyshev polynomials [22, 24] and Legendre polynomials [25].”