Fredholm integral equations are a type of integral equation that involve an unknown function, which is typically solved for in mathematical problems. They can be expressed in the form f(x) = g(x) + \lambda \int K(x, y) u(y) dy , where K(x, y) is a known kernel function, g(x) is a given function, and \lambda is a parameter. These equations are often used in various fields such as physics, engineering, and statistics. 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 both the integral and the unknown function itself. Solutions to these equations can provide valuable insights into problems involving boundary value problems and potential theory.