Partial integral Fredholm equation in anisotropic classes of Lebesgue functions on $\mathbb{R}_2$

In this paper, we propose a formula for representing the solution of a partial integral Fredholm equation of the second kind in the form of the corresponding Neumann series. We obtain conditions for the existence and uniqueness of this solution in the classes of Lebesgue functions $L_{\boldsymbol{p}}$, $\boldsymbol{p}=(p_1,p_2)$, defined in a finite rectangle $D=(a_1,b_1 )\times(a_2,b_2)$ of the Euclidean space $\mathbb{R}_2$.