On fractal dimension of the graph of nonstationary fractal interpolation function

Abstract

This article aims to study fractal dimension of the nonstationary fractal interpolation function (FIF) on function spaces. We estimate the Hausdorff dimension and the box dimension of nonstationary FIF on convex-Lipschitz space. We also compute the upper box dimension of the nonstationary FIF on oscillation spaces. Furthermore, we study the fractal dimension of the nonstationary FIF and the Katugampola fractional integral on Hölder space and bounded variational space.