Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus

Mi-Gyong Ri, Chol-Hui Yun and Myong-Hun Kim

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: In this paper, we construct a cubic spline hidden variable recurrent fractal interpolation function(CSHVRFIF) and prove that its Riemann-Liouville fractional integral and derivative are also HVRFIFs. To do it, firstly, we calculate calculus of hidden variable recurrent fractal interpolation function(HVRFIF) and give a theorem on the existence of Cr-HVRFIF. Secondly, we construct CSHVRFIFs of Type-Ⅰ and Type-Ⅱ, cardinal CSHVRFIFs and estimate error bound between the constructed CSHVRFIF and an original function. Finally, we insist that fractional calculus of cardinal CSHVRFIFs are also HVRFIFs.

Keywords: Recurrent iterated function system; Spline interpolation; Hidden variable fractal interpolation function; Fractional derivative; Fractional integral (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005312

DOI: 10.1016/j.chaos.2021.111177

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