Fractional integral approach on nonlinear fractal function and its application

C. Kavitha; A. Gowrisankar; C. Kavitha; A. Gowrisankar

doi:10.3934/mmc.2024019

Mathematical Modelling and Control

2024, Volume 4, Issue 3: 230-245. doi: 10.3934/mmc.2024019

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Fractional integral approach on nonlinear fractal function and its application

C. Kavitha ,
A. Gowrisankar ^,

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India

Received: 20 January 2024 Revised: 11 March 2024 Accepted: 07 May 2024 Published: 28 June 2024

The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigated the fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotch contraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of the Riemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal function theory 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.
- iterated function system,
- Rakotch contraction,
- fractal interpolation function,
- Riemann-Liouville fractional integral
Citation: C. Kavitha, A. Gowrisankar. Fractional integral approach on nonlinear fractal function and its application[J]. Mathematical Modelling and Control, 2024, 4(3): 230-245. doi: 10.3934/mmc.2024019

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Abstract

The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigated the fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotch contraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of the Riemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal function theory 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.

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