Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative

Abstract

In this manuscript, we consider the problem of regional boundary observability for semilinear time-fractional systems involving the Riemann-Liouville fractional derivative. Our primary goal is to focus on reconstructing the initial state in the desired subregion located on the boundary of the spatial domain. To do that, we firstly construct a link between regional boundary observability of the considered semilinear system and regional observability of its linear part. And with the help of an extension of the Hilbert uniqueness method (HUM), we recover the value of the initial state on the desired boundary subregion. We also provide a numerical simulation based on the steps of the HUM approach that shows the proposed algorithm’s efficiency and backs up our theoretical results.

Keywords:

• Control theory
• Hilbert uniqueness method
• regional boundary observability
• Riemann-Liouville derivative
• semilinear fractional systems
• time-fractional systems

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 93B07
• 93B28
• 26A33
• 46F12

Acknowledgments

This paper is in memory of the late professor Ali Boutoulout from Moulay Ismail University - Faculty of Sciences in Meknes - Morocco, who contributed vividly to the realization of this work.