IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921005312.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921005312
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111177?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. XueZai Pan, 2014. "Fractional Calculus of Fractal Interpolation Function on," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
    2. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yao, Kui & Chen, Haotian & Peng, W.L. & Wang, Zekun & Yao, Jia & Wu, Yipeng, 2021. "A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Yu, Binyan & Liang, Yongshun, 2024. "On two special classes of fractal surfaces with certain Hausdorff and Box dimensions," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    3. Prasad, S.A. & Verma, S., 2023. "Fractal interpolation function on products of the Sierpiński gaskets," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Tyada, K.R. & Chand, A.K.B. & Sajid, M., 2021. "Shape preserving rational cubic trigonometric fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 866-891.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005312. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.