Highlights  Approximations of the fractional integro-differential equations are obtained.  Fractional integration operational matrix of Legendre wavelets is derived.  Reducing the initial problem to a system of algebraic equations.  Solving the system of algebraic equations, the approximations are got. Abstract: In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in

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... Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration for Legendre wavelets. The application of this matrix for solving initial problem is explained. The mentioned equations are transformed into a system of algebraic equations. The error analysis of the proposed method is investigated. Finally, some numerical examples are shown to illustrate the efficiency of the approach.