Controllability of a backward fractional semilinear differential equation

In this paper we study the approximate controllability of a fractional semilinear differential equation involving the right fractional Caputo derivative. More precisely, we construct by means of Tikhonov type regularization method, the controllability operator. Then under certain condition on this operator, we obtain that the associate backward fractional linear system can be steered to an arbitrary small neighborhood of the state at initial time. This allows us to prove the approximate controllability of the semilinear system.