The mathematical description of the dynamical processes encountered in physical, biological, and applied sciences nowadays requires the investigation of (ordinary and partial) differential equations, equations with delay, integral or integro-differential equations, and other kinds of functional equations,
The first integral equation mentioned in the mathematical literature is due to Abel and can be found in almost any book on this subject (see, for instance, the author's book [12]), Abel found this equation in 1812, starting from a problem in mechanics. He gave a very elegant solution that was published in 1826 in Crelle's Journal.