We consider a controlled fractional diffusion wave equation involving Riemann-Liouville fractional derivative or order α ∈ (1, 2). First we prove by means of eigenfunction expansions the existence of solutions to such equations. Then we show that we can approach the fractional integral of order 2 − α of the state at final time by a desired state by acting on the control. Using the first order Euler-Lagrange optimality, we obtain the characterization of the optimal control.