Simulation studies on the boundary stabilization and disturbance rejection for fractional diffusion-wave equation

A class of evolution systems described by the one-dimensional fractional diffusion-wave equation subject to a boundary controller at the boundary is considered. Both boundary stabilization and disturbance rejection are considered. This paper, for the first, has confirmed, via hybrid symbolic and numerical simulation studies, that the existing two schemes for boundary stabilization and disturbance rejection for (integer order) wave/beam equations are still valid for fractional order diffusion-wave equations. The problem definition, the hybrid symbolic and numerical simulation techniques, outlines of the methods for boundary stabilization and disturbance rejection are presented together with extensive simulation results. Different dynamic behaviors are revealed for different fractional orders which create new future research opportunities.