In the field of fractal geometry, fractal interpolation functions have got a variety of interesting applications not only in the mathematical sciences but also in other areas of applied sciences, for instance [1–5]. The fractal interpolation function has been introduced with the aim of analyzing rough functions (or data) in the real world. Comparing with traditional interpolants, fractal interpolants seem to be more flexible. The reason behind the feasibility is that FIFs can be utilized for the best approximation of complicated mathematical structures with simple iterative procedure. As discussed in Chapter 2 , Barnsley has interpreted the fractal interpolation function in two ways: (i) FIF as an attractor of the iterated function system, (ii) FIF as a fixed point of the Read-Bajraktarević operator defined on a suitable complete space of \(\mathbb {R}\) . Moreover, in general, fractal functions are not always differentiable, as a consequence classical differentiation cannot be applied to them. Nevertheless, the integral of fractal functions can be studied since they are continuous everywhere and bounded.