Construction of New Fractal Interpolation Functions Through Integration Method

This paper investigates the classical integral of various types of fractal interpolation functions namely linear fractal interpolation function, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-fractal function and hidden variable fractal interpolation function with function scaling factors. The integral of a fractal function is again a fractal function to a different set of interpolation data if the integral of fractal function is predefined at the initial point or end point of the given data. In this study, the selection of vertical scaling factors as continuous functions on the closed interval of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document} provides more diverse fractal interpolation functions compared to the fractal interpolations functions with constant scaling factors.