This article explores the properties of fractal interpolation functions with variable scaling parameters, in the context of smooth fractal functions. The first part extends the Barnsley-Harrington theorem for differentiability of fractal functions and the fractal analogue of Hermite interpolation to the present setting. The general result is applied on a special class of iterated function systems in order to develop differentiability of the so-called -fractal functions. This leads to a bounded linear map on the space which is exploited to prove the existence of a Schauder basis for consisting of smooth fractal functions. © 2015 Australian Mathematical Publishing Association Inc.