Fredholm integral equations

Fredholm integral equations are a type of mathematical equation where an unknown function appears inside an integral, which is a sum or accumulation process. Basically, they relate the value of a function at a certain point to an integral involving that same function over a range. These equations often appear in physics, engineering, and mathematics when modeling systems with spatial or temporal interactions, such as wave behavior or heat transfer. Solving them involves finding the function that satisfies the integral relationship, often through specific methods or approximations. They provide a way to understand complex systems where current states depend on an aggregated effect of prior or surrounding states.