Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension

Mi-Gyong Ri and Chol-Hui Yun

Chaos, Solitons & Fractals, 2022, vol. 156, issue C

Abstract: In [M.G. Ri and C.H. Yun, Smoothness and fractional integral of hidden variable recurrent fractal interpolation function with function vertical scaling factors, Fractals 29(6) (2021) 2150136], the authors proved that the partial and mixed Riemann-Liouville fractional integrals of bivariable hidden variable recurrent fractal interpolation function(HVRFIF) with function scaling factors are HVRFIFs. As its continuation, in this paper, we show that Riemann-Liouville fractional derivatives of one variable and bivariable HVRFIFs are HVRFIFs under certain conditions. We also derive the relationship between the order of fractional calculus and the upper box dimension of its graph. To do it, firstly, we prove that Riemann-Liouville fractional derivative of one variable HVRFIF is HVRFIF. Secondly, we obtain estimation of the upper box dimension of the graph of one variable HVRFIF and derive the relationship between the upper box dimension and the order of fractional calculus. Finally, in the similar way to one variable, we show that the partial and mixed Riemann-Liouville fractional derivatives of bivarible HVRFIF are HVRFIFs.

Keywords: Recurrent iterated function system; Hidden variable fractal interpolation function; Box dimension; Riemann-Liouville fractional derivative; MSC: 28A80; 26A33; 41A05 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922000042
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000042

DOI: 10.1016/j.chaos.2022.111793

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().