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In this paper, linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations are solved by Variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivative is considered in the Caputo sense . The solutions of both problems are derived by infinite convergent series . Numerical example are presented to illustrate the efficiency and reliability of two methods. General TermsNumerical solutions, Fractional integro-differential equations.

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In this paper we investigate the numerical solution of Abel's integral equations of the first and second kind by chebychev polynomials of the first ,second ,third and fourth kinds. Some numerical examples are presented to illustrate the method.