doi:10.3390/fractalfract6100602engNavascués, María A.Pacurar, CristinaDrakopoulos, VasileiosScale-free fractal interpolationART-2022-130659An iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal interpolation functions associated with Matkowski contractions for finite as well as infinite (countable) sets of data are obtained. Furthermore, we construct an extension of the concept of α-fractal interpolation functions, herein called R-fractal interpolation functions, related to a finite as well as to a countable iterated function system and provide approximation properties of the R-fractal functions. Moreover, we obtain smooth R-fractal interpolation functions and provide results that ensure the existence of differentiable R-fractal interpolation functions both for the finite and the infinite (countable) cases.2022http://zaguan.unizar.es/record/11982310.3390/fractalfract6100602http://zaguan.unizar.es/record/119823oai:zaguan.unizar.es:119823Fractal and fractional 6, 10 (2022), 602 [15 pp]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess