ABSTRACT
Fredholm integral equation represents in mathematics an integral equation whose solutions have to give rise to Fredholm theory, Fredholm nuclei study, and Fredholm operators. Fredholm integral equation was the basis of Fredholm’s theorems, one of them being known as Fredholm alternative. The Fredholm alternative can be expressed in various ways, i.e., as a linear algebraic theorem, as a theorem of integral equations or as theorem based on Fredholm operators. A lot of solution techniques are nowadays available to solve the Fredholm integral equations. The numerical solutions of Volterra-Fredholm non-linear integral equation were studied, by product integration method. Thus, the equations could be transformed in a non-linear algebraic system, which could be solved by classical methods. The applicability of the Fredholm integral equation was demonstrated in several domains, such as applied mathematics, physics, chemistry and engineering. Fredholm integral equation was discovered in mathematics and consist the basis for the further development of the integral equation theory.
