Fractional integral approach on nonlinear fractal function and its application
The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigatedthe fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotchcontraction. We demonstrated how...
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AIMS Press
2024-06-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024019 |
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| author | C. Kavitha A. Gowrisankar |
| author_facet | C. Kavitha A. Gowrisankar |
| author_sort | C. Kavitha |
| collection | DOAJ |
| description | The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigatedthe fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotchcontraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of theRiemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal functiontheory was elucidated based on a comparative analysis of the irregularity relaxation process. Moreover, a reconstitution of epidemic curves from the perspective of a nonlinear fractal interpolation function was presented, and a comparison between the graphs of linear and nonlinear fractal functions was discussed. |
| format | Article |
| id | doaj-art-9d9cbf569ae34aa4a14543477a2cca60 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-9d9cbf569ae34aa4a14543477a2cca602025-01-24T01:02:08ZengAIMS PressMathematical Modelling and Control2767-89462024-06-014323024510.3934/mmc.2024019Fractional integral approach on nonlinear fractal function and its applicationC. Kavitha0A. Gowrisankar1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaThe shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigatedthe fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotchcontraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of theRiemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal functiontheory was elucidated based on a comparative analysis of the irregularity relaxation process. Moreover, a reconstitution of epidemic curves from the perspective of a nonlinear fractal interpolation function was presented, and a comparison between the graphs of linear and nonlinear fractal functions was discussed.https://www.aimspress.com/article/doi/10.3934/mmc.2024019iterated function systemrakotch contractionfractal interpolation functionriemann-liouville fractional integral |
| spellingShingle | C. Kavitha A. Gowrisankar Fractional integral approach on nonlinear fractal function and its application Mathematical Modelling and Control iterated function system rakotch contraction fractal interpolation function riemann-liouville fractional integral |
| title | Fractional integral approach on nonlinear fractal function and its application |
| title_full | Fractional integral approach on nonlinear fractal function and its application |
| title_fullStr | Fractional integral approach on nonlinear fractal function and its application |
| title_full_unstemmed | Fractional integral approach on nonlinear fractal function and its application |
| title_short | Fractional integral approach on nonlinear fractal function and its application |
| title_sort | fractional integral approach on nonlinear fractal function and its application |
| topic | iterated function system rakotch contraction fractal interpolation function riemann-liouville fractional integral |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024019 |
| work_keys_str_mv | AT ckavitha fractionalintegralapproachonnonlinearfractalfunctionanditsapplication AT agowrisankar fractionalintegralapproachonnonlinearfractalfunctionanditsapplication |