CONSTRUCTION OF NEW AFFINE AND NON-AFFINE FRACTAL INTERPOLATION FUNCTIONS THROUGH THE WEYL–MARCHAUD DERIVATIVE

T. M. C. Priyanka () and A. Gowrisankar
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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

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-15

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.

Keywords: Iterated Function System; Fractal Interpolation Function; Weyl–Marchaud Fractional Derivative; Function Scaling Factors (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2350041X

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