Solvability and Weak Controllability of Fractional Degenerate Singular Problem

—In this paper, our objective is to investigate the unique solvability and the weak controllability of the fractional degenerate and singular problem. The energy inequality method is gives a sufficient conditions for the existence and the uniqueness of the strong solution of our problem. This problem is ill-posed in the sense of Hadamard. To address this, we attempt regularization through a fractional Tikhonov regularization method, which not only establishes weak controllability but also provides a full characterization of the optimal control.