Analysis of non-linear fractal functions on PCF self-similar sets

Abstract

This article deals with (1) the construction of a general non-linear fractal interpolation function on PCF self-similar sets, (2) the energy and normal derivatives of uniform non-linear fractal functions, (3) estimation of the bound of box dimension of the proposed fractal functions on the Sierpinski gasket and the von-Koch curve. Here, we present a more general framework to construct the attractor and the functions on the PCF self-similar sets using the Edelstein contraction, which broadens the class of functions. En route, we calculate the upper and lower box dimensions of the graph of non-linear interpolant. Finally, we provide several graphical and numerical examples for illustration of the construction and estimate the dimensions for different data sets.