A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile

Abstract

The goal of this paper project is to find a minimum time null controllability of the fractional heat equation in one dimension using the notion of strategic zone actuators. As part of our research activities, we had already addressed this theme, and this publication project is a logical continuation in the fractional case. Thus, this work has already been done in the case of classical differentiability in the sense of Frèchet. Indeed, inspired by the work of Khodja and Seck on the null controllability of the 1D heat equation and that of El Jai on the spreadability by means of the use of strategic actuators called zones, we have managed to decrease the minimum null controllability time of the 1D fractional heat equation. We are well aware of the difficulties linked to establishing the coercivity inequality of the parabolic operator. This requires searching for other, more innovative control methods. This is how, in this project, a mixed method using the method of moments and the notion of strategic profile was used to find a better minimum time of null controllability of the 1D fractional heat equation on regular domains by compared to what is known in the literature.