In this paper, we studied the existence and uniqueness result of solutions for boundary value problems for Hilfer-Hadamard type fractional differential inclusions with multi-point boundary conditions, in the first approach we deal with a non-convex valued right hand side and in the second approach we consider the Carath\’eodory case. Finally the compactness of solution sets is also obtained.

The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial conditions. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel-Legendre transform and appropriate Carleman inequalities.