Volterra integral equation of the first kind

A Volterra integral equation of the first kind relates an unknown function to its history through an integral, meaning the current value depends on the accumulation of past values. Imagine measuring a quantity where each measurement is influenced by all previous measurements, weighted in a specific way. Mathematically, it looks like an equation where the unknown function is inside an integral that extends over past points. These equations are common in modeling systems where history influences present behavior, such as in physics, biology, or engineering. Solving them means finding the original function based on how it accumulates over time.