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Construction Of New Affine And Non-Affine Fractal Interpolation Functions Through The Weyl–Marchaud Derivative

Author

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  • T. M. C. PRIYANKA

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

  • A. GOWRISANKAR

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

Abstract

This paper investigates the Weyl–Marchaud fractional derivative of affine and non-affine fractal interpolation functions with function scaling factors. The dependence of fractal interpolation function on the scaling factor is mainly explored by choosing the scaling factor as a function instead of a constant. In addition, for some fixed order v, the Weyl–Marchaud fractional derivative of a linear fractal interpolation function is estimated by predefining the fractional derivative values at the end points. Similarly, the Weyl–Marchaud fractional derivative of a α-fractal function is investigated for some fixed order v with additional constraints on the derivative of prescribed continuous function and base function.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x2350041x
    DOI: 10.1142/S0218348X2350041X
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    Cited by:

    1. 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.

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