Fredholm equations are a type of integral equation that arise in various fields such as physics and engineering. They are named after the Swedish mathematician Erik Fredholm, who studied these equations in the early 20th century. A typical Fredholm equation involves an unknown function that is expressed as an integral involving a known kernel function and a given function. There are two main types of Fredholm equations: the first kind and the second kind. The first kind involves solving for the unknown function directly from the integral, while the second kind includes an additional term that represents a known function. These equations are important for understanding boundary value problems and other applications in mathematical analysis.