The present paper aims to introduce a new concept of a non-stationary scheme for the so called fractal functions. Here we work with a sequence of maps for the zipper iterated function systems (IFS). We show that the proposed method generalizes the existing stationary interpolant in the sense of IFS. Further, we study the elementary properties of the proposed interpolant and calculate its box and Hausdorff dimension. Also, we obtain an upper bound of the graph of the fractional integral of the proposed interpolant. We notice that the box dimension of the graph of the proposed interpolant is independent of the signature value for a fixed scale vector. In the end, using the method of fractal perturbation of a given function, we construct the associated fractal operator and study some of its properties.

本文旨在为所谓的分形函数引入一个非平稳方案的新概念。在这里，我们使用拉链迭代函数系统 (IFS) 的一系列映射。我们表明，所提出的方法在 IFS 的意义上推广了现有的固定插值。此外，我们研究了所提出的插值的基本性质，并计算了它的盒子和豪斯多夫维数。此外，我们获得了所提出的插值的分数积分图的上限。我们注意到，所提出的插值图的框尺寸与固定比例向量的特征值无关。最后，利用给定函数的分形扰动方法，构造了相关的分形算子，并研究了它的一些性质。