ENERGY CONSIDERATIONS FOR FRACTIONAL ELEMENTS

This paper considers the energy aspects of fractional elements defined by the equation F(t) = k(lambda) {0D(t)(lambda)x(t)}. In contrast to the typically conservative assumption of classical physics that lead to the potential and kinetic energy expressions, a number of important non-conservative differences are exposed. Firstly, the considerations must be time-based rather than displacement or momentum based variables. Time based equations for energy behavior of fractional elements are presented and example applications are considered. The effect of fractional order on the energy requirements and energy return of these systems is shown. Importantly, it is shown that the history, or initialization, has a strong effect on energy requirements. Finally, compact expressions for the work or energy, are developed.