Fractalization of Fractional Integral and Composition of Fractal Splines

Yıl 2023, Cilt: 5 Sayı: 4, 318 - 325, 31.12.2023

Gowrisankar Arulprakash

https://doi.org/10.51537/chaos.1334407

Öz

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.

Anahtar Kelimeler

Fractional integral, α-fractal function, Error estimation, Composite fractal functions

Kaynakça

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