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In this article, we present a numerical method to numerically solve a time-fractional convection–diffusion equation. Our method is based on the operational matrices of shifted Jacobi polynomials. At first, problem is converted to a homogeneous problem by interpo- lation and afterward an integro-differential equation is yielded. Then we approximate the known and unknown functions with the help of shifted Jacobi functions. A system of non- linear algebraic equations is obtained. Finally, the unknown coefficients are determined by Mathematica TM . We implemented the proposed method for several examples that they in- dicate the high accuracy method. It should be noted that this method is generalizable to some appropriate problems.
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