On fractal rational functions

This article introduces fractal perturbation of classical rational functions via α-fractal operator and investigates some aspects of this new function class, namely, the class of fractal rational functions. Its specific aims are: (1) to define the fractal rational functions along the lines of the fractal polynomials (2) to extend the Weierstrass theorem of uniform approximation to fractal rational functions (3) to deduce a fractal version of the classical Müntz theorem on rational functions (4) to prove the existence of a Schauder basis for C.I/consisting of fractal rational functions.