Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
19 December 2019 |
03 January 2020 |
10 March 2020 |
Abstract: Control theory is one of the essential domains of studies in mathematics, it serves as a link between applied mathematics and technology, it includes various notions, which are very useful in many fields of engineering, such as Controllability, Stability and Observability. For us, we are interested in a global version of only the last concept, namely "Regional Observability", and we are investigating it for a special type of systems called fractional order systems. Many works have been done in this subject for both linear and semilinear classical "integer order" systems. The reason behind our interest in fractional or non-integer order systems is that, it had been proven in the last few years that these kind of systems can be better in modeling real world phenomena compared to classical systems. In this work we study the regional observability problem more precisely the regional reconstruction of the initial state for a given time fractional semilinear systems using an extension of the famous Hilbert Uniqueness Method (HUM).
