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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| Format: | Article |
| Language: | English |
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Akif AKGUL
2023-12-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3294088 |
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| author | Gowrisankar Arulprakash |
| author_facet | Gowrisankar Arulprakash |
| author_sort | Gowrisankar Arulprakash |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b236f399f9c447d990dd51a1b8761cd9 |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-b236f399f9c447d990dd51a1b8761cd92025-01-23T18:15:39ZengAkif AKGULChaos Theory and Applications2687-45392023-12-015431832510.51537/chaos.13344071971Fractalization of Fractional Integral and Composition of Fractal SplinesGowrisankar Arulprakash0https://orcid.org/0000-0002-5093-2805Vellore Institute of Technology, VelloreThe 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.https://dergipark.org.tr/en/download/article-file/3294088fractional integralα-fractal functionerror estimationcomposite fractal functions |
| spellingShingle | Gowrisankar Arulprakash Fractalization of Fractional Integral and Composition of Fractal Splines Chaos Theory and Applications fractional integral α-fractal function error estimation composite fractal functions |
| title | Fractalization of Fractional Integral and Composition of Fractal Splines |
| title_full | Fractalization of Fractional Integral and Composition of Fractal Splines |
| title_fullStr | Fractalization of Fractional Integral and Composition of Fractal Splines |
| title_full_unstemmed | Fractalization of Fractional Integral and Composition of Fractal Splines |
| title_short | Fractalization of Fractional Integral and Composition of Fractal Splines |
| title_sort | fractalization of fractional integral and composition of fractal splines |
| topic | fractional integral α-fractal function error estimation composite fractal functions |
| url | https://dergipark.org.tr/en/download/article-file/3294088 |
| work_keys_str_mv | AT gowrisankararulprakash fractalizationoffractionalintegralandcompositionoffractalsplines |