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On the integral transform of fractal interpolation functions

Author

Listed:
  • Agathiyan, A.
  • Gowrisankar, A.
  • Fataf, Nur Aisyah Abdul

Abstract

This paper explores the integral transform of two distinct fractal interpolation functions, namely the linear fractal interpolation function and the hidden variable fractal interpolation function with variable scaling factors. Further, with a particular application of kernel functions, we investigate the integral transform of fractal functions, such as the Laplace transform and the Laplace Carson transform. Moreover, we show that the compositeness of two fractal interpolation functions, f1 in {tɛ,xɛ} and f2 in {xɛ,zɛ} remains a fractal interpolation function. It also generates iterated function system from given iterated function systems. In addition to this, the study is carried out on the composite linear fractal interpolation function of the integral transform, the Laplace transform, and the Laplace Carson transform.

Suggested Citation

  • Agathiyan, A. & Gowrisankar, A. & Fataf, Nur Aisyah Abdul, 2024. "On the integral transform of fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 209-224.
    • Handle: RePEc:eee:matcom:v:222:y:2024:i:c:p:209-224
    DOI: 10.1016/j.matcom.2023.08.018
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    References listed on IDEAS

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    1. Prithvi, B.V. & Katiyar, S.K., 2022. "Interpolative operators: Fractal to multivalued fractal," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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    4. Yun, CholHui & Ri, MiGyong, 2020. "Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Y. S. Liang, 2022. "Approximation With Fractal Functions By Fractal Dimension," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-12, November.
    6. Subhash Chandra & Syed Abbas, 2021. "The Calculus Of Bivariate Fractal Interpolation Surfaces," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-13, May.
    7. Dai, Zhong & Liu, Shutang, 2023. "Construction and box dimension of the composite fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. T. M. C. Priyanka & A. Gowrisankar, 2023. "Construction Of New Affine And Non-Affine Fractal Interpolation Functions Through The Weyl–Marchaud Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-15.
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