Regional controllability of anomalous diffusion generated by the time fractional diffusion equations

Abstract

This paper is concerned with the investigation of the regional controllability of the time fractional diffusion equations. First, some preliminaries and definitions of regional controllability of the system under consideration are introduced, which promote the existence contributions on controllability analysis. Then we analyze the regional controllability with minimum energy of the time fractional diffusion equations on two cases: $B\in \mathbf{L}\left(\mathbf{R}^m, L^2(\Omega) \right)$ and $B\notin \mathbf{L}\left(\mathbf{R}^m, L^2(\Omega) \right)$. In the end, two applications are given to illustrate our obtained results.