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The Calculus Of Bivariate Fractal Interpolation Surfaces

Author

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  • SUBHASH CHANDRA

    (School of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175005, India)

  • SYED ABBAS

    (School of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175005, India)

Abstract

In this paper, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions (FIFs). We also prove that the mixed Riemann–Liouville fractional integral and derivative of order γ = (p,q); p > 0,q > 0, of bivariate FIFs are again bivariate interpolation functions corresponding to some iterated function system (IFS). Furthermore, we discuss the integral transforms and fractional order integral transforms of the bivariate FIFs.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500663
    DOI: 10.1142/S0218348X21500663
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    Citations

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    Cited by:

    1. Gupta, Deepika & Pandey, Asheesh, 2024. "Analyzing impact of corporate governance index on working capital management through fractal functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Verma, Shubham Kumar & Kumar, Satish, 2024. "Fractal dimension analysis of financial performance of resulting companies after mergers and acquisitions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. 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.
    5. Verma, S. & Jha, S. & Navascués, M.A., 2023. "Smoothness analysis and approximation aspects of non-stationary bivariate fractal functions," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Lal, Rattan & Chandra, Subhash & Prajapati, Ajay, 2024. "Fractal surfaces in Lebesgue spaces with respect to fractal measures and associated fractal operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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