Solvability and Weak Controllability of Fractional Degenerate Singular Problem

Fatma, Achab
Batiha, Iqbal
Imad, Rezzoug
Takieddine, Oussaeif
Ouannas, Adel

Journal of Robotics and Control (JRC)
Vol 5, No 2 (2024)

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.