A Dynamic-Order Fractional Dynamic System

Motivated by the experimental result of an electronic circuit element "fractor", we introduce the concept of a 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 concept offers an explanation for the physical mechanism of variable-order fractional dynamic systems and multi-system interaction. The properties and potential applications of dynamic-order fractional dynamic systems are further explored by analyzing anomalous relaxation and diffusion processes.