Reference tracking problem for boundary controlled time fractional advection dispersion equation in the presence of disturbances

In this paper, the output regulation problem of the time fractional advection-dispersion equation is considered, in the presence of disturbances. A generalized backstepping method is designed to allow the output to track a desired trajectory by manipulating the system’s control input located at the boundary. In addition, the paper provides the fundamental solution of the considered problem and the proof of its uniqueness.