Physical and geometrical interpretation of fractional operators

✍ Scribed by M. Moshrefi-Torbati; J.K. Hammond

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 737 KB
• Volume: 335
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(97)00048-3

✦ Synopsis

In this paper an interpretation offractional 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 realisation of fractional operators. It is concluded here that fractional operators ma-v be grouped as jilters with partial memory that fall between two extreme types qf filters with complete memory and those with no memory. Fractional operators are capable qf modelling 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. Similarl_v, the fractional order of a differentiator reflects the rate at which a portion qf the energy has been lost.