A Dynamic-Order Fractional Dynamic System
  Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the differential-order of a fractional dynamic system is determined by the output signal of another dynamic system. The new concept offers a comprehensive explanation of physical mechanism of multi-system interaction. The properties and potential applications of dynamic-order fractional dynamic systems are further explored with the analysis of anomalous relaxation and diffusion processes. 
HongGuang Sun, Hu Sheng, YangQuan Chen, Wen Chen and ZhongBo Yu
math-ph math.MP physics.flu-dyn