FREDHOLM INTEGRAL EQUATIONS AND ITS CONSEQUENCES

In the field of Integral Equations, Fredholm Integral Equations play a central role in both pure and applied mathematics. They arise naturally in many areas such as Physics, Engineering and Mathematical Analysis, especially when dealing with Boundary Value Problems. A Fredholm Integral Equation is an equation in which the unknown function appears under an integral sign and the limits of Integration under are Fixed (Constant). The study of Fredholm Integral Equations was introduced by the Swedish mathematician Erik Ivar Fredholm in the early 20th century. His Work laid the foundation for modern functional analysis and contributed significantly to solving complex physical problems. He developed the theory of Kernels and determinants to study existence and uniqueness of solutions.