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In this paper, we present a new analytical technique for obtaining the analytical approximate solutions for system of Fredholm integral equations based on the use of the residual power series method (RPSM). The proposed method provides the solution in terms of convergent series with easily computable components, as well as it possesses main advantage as compared to other existed methods; it can be applied without any limitation or linearization on the nature of the problem, type of classification, and the number of mesh points. In this sense, some examples are given to demonstrate the simplicity and efficiency of the proposed method. The results obtained by employing the RPSM are compared with exact solutions to reveal that the method is easy to implement, straightforward and convenient to handle a wide range of such system of integral equations.

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