Fractalization of Fractional Integral and Composition of Fractal Splines
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Akif AKGUL
2023-12-01
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| Series: | Chaos Theory and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/3294088 |
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| Summary: | 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. |
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| ISSN: | 2687-4539 |