This article explores the construction of a more general type of multivariate \(\alpha \) -fractal functions. The construction is based on the notion of a non-stationary iterated function system, which generalizes the classical case (the stationary one). At first, we construct the associated fractal functions on the space of all continuous functions defined on a hyper-rectangle of \({\mathbb {R}}^n\) and on the space of all continuous functions that are differentiable several times. Furthermore, we observe that the perturbation method provides an operator that obeys many topological properties, similar to those in the stationary multivariate case. Also, this operator can help to create and analyze non-stationary fractals with controlled properties. Additionally, we estimate the upper bound of the dimension of the proposed interpolant after constructing it on the Hölder space. Finally, we calculate the bounds of the dimension of the Riemann–Liouville fractional integral of the multivariate non-stationary \(\alpha \) -fractal functions.
