With the aid of fixed-point theorem (an equivalent version for the linear case) and biorthogonal systems in adequate Banach spaces, the problem of approximating the solution of a linear Fredholm-Volterra integro-differential equation is turned into a numerical algorithm, so that it can be solved numerically.
"Fixed-Point Iterative Algorithm for the Linear Fredholm-Volterra Integro-Differential Equation." J. Appl. Math. 2012 (SI03) 1 - 12, 2012. https://doi.org/10.1155/2012/370894