Fredholm Integral Equations are a type of integral equation that involve an unknown function, which is typically solved for in terms of an integral. They can be expressed in the form f(x) = \lambda \int K(x, y) g(y) dy + h(x) , where K(x, y) is a known kernel function, \lambda is a parameter, and h(x) is a known function. These equations are often used in various fields such as physics, engineering, and mathematics to model complex systems. There are two main types of Fredholm Integral Equations: the first kind and the second kind. The first kind involves only the integral of the unknown function, while the second kind includes an additional term that is a function of the unknown. Solutions to these equations can be found using various methods, including numerical techniques and analytical approaches, depending on the specific