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This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M −κ ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.Mathematics Subject Classification. Primary 26A33; Secondary 65L05.

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