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

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

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.

Suggested Citation

  • Ri, Mi-Gyong & Yun, Chol-Hui & Kim, Myong-Hun, 2021. "Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005312
    DOI: 10.1016/j.chaos.2021.111177
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    References listed on IDEAS

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    1. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Katiyar, S.K. & Chand, A. K. B & Saravana Kumar, G., 2019. "A new class of rational cubic spline fractal interpolation function and its constrained aspects," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 319-335.
    3. XueZai Pan, 2014. "Fractional Calculus of Fractal Interpolation Function on," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
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    Cited by:

    1. Ri, Mi-Gyong & Yun, Chol-Hui, 2022. "Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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