Regional controllability analysis of fractional diffusion equations with   Riemann-Liouville time fractional derivatives
  This paper is concerned with the concepts of regional controllability for the Riemann-Liouville time fractional diffusion systems of order $\alpha\in(0,1)$. The characterizations of strategic actuators to achieve regional controllability are investigated when the control inputs emerge in the differential equations as distributed inputs. In the end, an approach to guarantee the regional controllability of the problems under consideration in the considered subregion with minimum energy control is described and successfully tested through two applications. 
Fudong Ge, YangQuan Chen and Chunhai Kou
math.OC