ABSTRACT
Regional observability is a famous tool in the field of control theory; its goal is to search for and recover the value of the initial state for a given system in a chosen region of the whole spatial domain. The present chapter deals with the regional observability problem for a class of semilinear time-fractional systems employing the Riemann-Liouville time-fractional derivative. We extend the so-called Hilbert uniqueness method (HUM) to cover the fractional framework, where we transform the reconstruction problem into a fixed point one of a well-chosen functional. Built upon the HUM steps, we develop an algorithm that grants the regional recovery of the initial state. The proposed algorithm leads to a successful numerical simulation showing the attempted approach’s validity and efficiency.
