Fredholm equation. The solution of the Fredholm equation of the second kind with a continuous kernel can be reduced to the solution of two functional differential equations with Cauchy conditions. This fact suggests the idea of constructing solutions of integral equations in the form of power series. Let us consider the Fredholm equation (see article). Volterra equation. In this paragraph, we apply the above considerations to the Volterra equation. We will consider the equation (see article).

1. Fredholm equation. Let us consider integral equations of the form (1). Finally, we note that the proposed method can be easily generalized to the case of the system of integral equations. 2. Volterra equation. The above idea can be generalized to the Volterra equation of the second kind. Let us consider equation (23) (see the article). Thus, equation (23) is equivalent to two functional linear differential equations (33) and (37) with Cauchy conditions (34) and (38), and the solution of equation (23) will be obtained by the formula (see article).