New general solutions to linear Fredholm integro-differential equations and their applications on solving the boundary value problems

This paper introduces the ΔN general solution to linear Fredholm integro-differential equations and sets its properties. The conditions for existence of classical general solution and solvability criteria for the equation are provided. Necessary and sufficient conditions for solvability of linear boundary value problems are established. Algorithms for construction of the ΔN general solutions are obtained. This paper also proposes approximate and numerical methods to solve the boundary value problems.