Fractal Dimension and Fractional Calculus of Non-Stationary Zipper Α-Fractal Function

Abstract

The fractal interpolation functions with appropriate iterated function systems (IFSs) provide a method to perturb and approximate a continuous function on a compact interval I. This method produces a class of functions f α, named as α-fractal functions. As essential parameters of the IFS, the scaling factor α has important consequences in the properties of the function f α. In this talk, we discuss the α-fractal functions corresponding to the non-stationary zipper IFS. Here, we present a method to calculate an upper bound of the box and Hausdorff dimension of the proposed interpolant. Also, we provide an upper bound of the graph of the fractional integral of the proposed interpolant