Fractalization of Fractional Integral and Composition of Fractal Splines

Authors : Gowrisankar Arulprakash

Pages : 318-325

Doi:10.51537/chaos.1334407

View : 48 | Download : 53

Publication Date : 2023-12-31

Article Type : Research Paper

Abstract :The present study perturbs the fractional integral of a continuous function $f$ defined on a real compact interval, say $(\\mathcal{I}^vf)$ using a family of fractal functions $(\\mathcal{I}^vf)^\\alpha$ based on the scaling parameter $\\alpha$. To elicit this phenomenon, a fractal operator is proposed in the space of continuous functions, an analogue to the existing fractal interpolation operator which perturbs $f$ giving rise to $\\alpha$-fractal function $f^\\alpha$. In addition, the composition of $\\alpha$-fractal function with the linear fractal function is discussed and the composition operation on the fractal interpolation functions is extended to the case of differentiable fractal functions.
Keywords : Fractional integral, α fractal function, Error estimation, Composite fractal functions