Scale-Free Fractal Interpolation

An iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by nonlinear contraction, investigated here. In such manner, functions associated with Matkowski contractions for finite as well infinite (countable) sets of data are obtained. Furthermore, we construct an extension the concept ?-fractal functions, herein called R-fractal related to countable and provide approximation properties functions. Moreover, obtain smooth results ensure existence differentiable both cases.