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In this paper, we propose an efficient numerical method for ordinary differential equation with fractional order, based on Legendre-Gauss-Radau interpolation, which is easy to be implemented and possesses the spectral accuracy. We apply the proposed method to multi-order fractional ordinary differential equation. Numerical results demonstrate the effectiveness of the approach.doi:10.4028/www.scientific.net/amm.687-691.601 fatcat:h5kum7okqbb7rfk332pgi7u45q