Solving a system of integral equations by an analytic method

In this paper, the recurrent relation, for solving a system of linear and nonlinear Volterra and Fredholm integral equations by an analytic method, namely homotopy analysis method (HAM), is introduced. For the power-law nonlinearities, our strategy is directly applied and for the other kind of nonlinearities, it is necessary to rewrite them in the form of power-law nonlinearities. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. The efficiency of the approach will be shown by applying the procedure on some examples.