ANALYSIS ON WEYL–MARCHAUD FRACTIONAL DERIVATIVE FOR TYPES OF FRACTAL INTERPOLATION FUNCTION WITH FRACTAL DIMENSION

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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-24

Abstract: In this paper, the Weyl–Marchaud fractional derivative of various fractal interpolation functions (FIFs) like linear FIF, quadratic FIF, hidden variable FIF and α-FIF is investigated. Further, the fractal dimension of the quadratic FIF is estimated and it is compared with the order of the Weyl–Marchaud fractional derivative. Besides, this paper shows that the Weyl–Marchaud fractional derivative of all FIFs is again FIFs if the order of the fractional derivative meets the necessary condition.

Keywords: Fractal Interpolation Function; Iterated Function System; Fractal Dimension; Weyl–Marchaud Fractional Derivative (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502157

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