A Physical experimental study of variable-order fractional integrator and differentiator

作者:Sheng, H.*; Sun, H. G.; Coopmans, C.; Chen, Y. Q.; Bohannan, G. W.
来源:The European Physical Journal - Special Topics, 2011, 193(1): 93-104.
DOI:10.1140/epjst/e2011-01384-4

摘要

Recent research results have shown that many complex physical phenomena can be better described using variable-order fractional differential equations. To understand the physical meaning of variable-order fractional calculus, and better know the application potentials of variable-order fractional operators in physical processes, an experimental study of temperature-dependent variable-order fractional integrator and differentiator is presented in this paper. The detailed introduction of analogue realization of variable-order fractional operator, and the influence of temperature to the order of fractional operator are presented in particular. Furthermore, the potential applications of variable-order fractional operators in (PID mu(t))-D-lambda(t) controller and dynamic-order fractional systems are suggested.