Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0989.26004
Moshrefi-Torbati, M.; Hammond, J.K.
Physical and geometrical interpretation of fractional operators. (English)
[J] J. Franklin Inst. 335B, No.6, 1077-1086 (1998). ISSN 0016-0032; ISSN 1879-2693/e

Summary: In this paper an interpretation of fractional operators in the time domain is given. The interpretation is based on the four concepts of fractal geometry, linear filters, construction of a Cantor set and physical realization of fractional operators. It is concluded here that fractional operators may be grouped as filters with partial memory that fall between two extreme types of filters with complete memory and those with no memory. Fractional operators are capable of modeling systems with partial loss or partial dissipation. The fractional order of a fractional integral is an indication of the remaining or preserved energy of a signal passing through such system. Similarly, the fractional order of a differentiator reflects the rate at which a portion of the energy has been lost.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
28A80 Fractals

Keywords: fractional derivative; Riemann-Liouville operator; fractal set; fractional operators; time domain; fractal geometry; linear filters; Cantor set; physical realization; fractional integral

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]