Zipper quintic fractal interpolation function for curve fitting

In this paper, we introduce a class of novel C2 -zipper rational quintic fractal interpolation functions (Zipper-RQFIF) with variable scalings in the form of a rational type that has a quintic polynomial in the numerator and a quadratic polynomial in the denominator with three shape control parameters. We restrict the scaling functions and shape control parameters so that the proposed Zipper-RQFIF is positive when the given dataset is positive. Using this sufficient condition, some numerical examples of positive Zipper-RQFIF are presented to support our theory. This paper approaches the zipper rational quintic fractal interpolation problem as a generalisation of both quintic fractal and affine zipper fractal interpolants, which show more versatility and flexibility than classical and fractal interpolation functions (FIFs). © 2024 Inderscience Enterprises Ltd.