On the integral transform of fractal interpolation functions

Abstract

This paper explores the integral transform of two distinct fractal interpolation functions, namely the linear fractal interpolation function and the hidden variable fractal interpolation function with variable scaling factors. Further, with a particular application of kernel functions, we investigate the integral transform of fractal functions, such as the Laplace transform and the Laplace Carson transform. Moreover, we show that the compositeness of two fractal interpolation functions, f1 in {tɛ,xɛ} and f2 in {xɛ,zɛ} remains a fractal interpolation function. It also generates iterated function system from given iterated function systems. In addition to this, the study is carried out on the composite linear fractal interpolation function of the integral transform, the Laplace transform, and the Laplace Carson transform.