On the controllability of fractional semilinear systems via the generalized Hattaf fractional derivative

The purpose of this paper is to investigate the controllability of a semilinear system including the generalized Hattaf fractional GHF derivative. First, the Laplace transform is used to solve the GHF system. To study the controllability of linear GHF systems, we compute the fractional controllability Gramian matrix and we derive the sufficient conditions. Based on the controllability of the linear system and the Schauder fixed-point theorem, sufficient conditions for controllability are established using the fixed-point theory for semilinear GHF systems. Finally, an example is given to confirm our theoretical findings.