In fact, as we already discussed, the Riemann–StieltjesRiemann–Stieltjes integralIntegral, which can be thought of as an integral of a continuous function with respect to another continuous function, is the fundamental operator used to extend the classical and fractional differential and integral operators that are the subject of discussion in this book. We will notice that when the other function is differentiable or continuous, various important results have been found by authors who have studied this operator. We will offer a selection of recent findings that will be relevant to the other chapters in this book in this chapter. Just to refresh your memory, the Riemann sum is often the region that lies roughly under the function curve [1].