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Explicit relation between Fourier transform and fractal dimension of fractal interpolation functions

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Abstract

This paper provides an explicit representation for the Fourier transform of different kinds of fractal interpolation functions. The construction of fractal functions using the theme of iterated function system has merely provided the functional equation. The Fourier series over the fractal functions is explored in the literary analysis to provide an explicit structure; however, Fourier series can be only studied for the periodic functions. Henceforth, this study investigates the Fourier transform of fractal interpolation functions with function scaling factors to explicitly express both the periodic and non-periodic cases. In addition, formulae relating the fractal dimension and the Fourier transform of fractal functions are presented. Finally, this paper demonstrates the Riemann–Liouville fractional derivative of fractal interpolation functions.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632 014, India

    A. Agathiyan & A. Gowrisankar

  2. Cyber Security and Digital Industrial Revolution Centre, Universiti Pertahanan Nasional Malaysia, Kuala Lumpur, Malaysia

    Nur Aisyah Abdul Fataf

Authors
  1. A. Agathiyan
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  2. Nur Aisyah Abdul Fataf
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  3. A. Gowrisankar
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Correspondence to A. Gowrisankar.

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Agathiyan, A., Fataf, N.A.A. & Gowrisankar, A. Explicit relation between Fourier transform and fractal dimension of fractal interpolation functions. Eur. Phys. J. Spec. Top. 232, 1077–1091 (2023). https://doi.org/10.1140/epjs/s11734-023-00779-8

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