The relationship between the fractional integral and the fractal structure of a memory set

Fu-Yao Ren, Zu-Guo Yu, Ji Zhou, Alain Le Mehaute and Raoul R. Nigmatullin

Physica A: Statistical Mechanics and its Applications, 1997, vol. 246, issue 3, 419-429

Abstract: It is shown that there is no direct relation between the fractional exponent v of the fractional integral and the fractal structure of the memory set considered, v depends only the first contraction coefficient χ1 and the first weight P1 of the self-similar measure (or infinite self-similar measure) μ on the memory set. If and only if P1=χ1β (where β ∈ (0,1) is the fractal dimension of the memory set), v is equal to the fractal dimension of the memory set. It is also true that v is continuous about χ1 and P1.

Keywords: Flûx; Memory measure; Laplace transform; Memory set; Self-similar (or infinite self-similar) measure (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437197003531
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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:phsmap:v:246:y:1997:i:3:p:419-429

DOI: 10.1016/S0378-4371(97)00353-1

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().