Physical and geometrical interpretation of fractional operators

Abstract

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 realisation 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 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. Similarly, the fractional order of a differentiator reflects the rate at which a portion of the energy has been lost.