Regional controllability results for Riemann–Liouville fractional control systems

Abstract

In this paper, we consider the problem of regional controllability for semi-linear time-fractional sub-diffusion systems involving Riemann–Liouville fractional derivative. Our goal is to steering the considered system into a desired state only in a sub-region of the spatial domain. In order to do that, we adapt the standard Hilbert Uniqueness Method (HUM), developed in Lions and Magenes (1968), Lions (1988), for our kind of system and we use two fixed point theorem depend to proposed assumptions. We also present some numerical simulations that illustrate the effectiveness of the proposed method, where we consider respectively zone actuator and pointwise one.

Keywords

• Fractional calculus
• Sub-diffusion systems
• Semi-linear systems
• Regional controllability
• Fixed point theory
• Gronwall’s lemma