Controllability of infinite-dimensional conformable linear and semilinear systems

The current paper discusses the controllability of systems governed by infinite-dimensional linear and semilinear conformable differential equations. By stating conformable controllability map, we provide necessary and sufficient conditions of the exact and approximative controllability for the conformable fractional linear system. Using Schauder’s fixed point theorem and assuming that the associated linear system is approximately controllable, we derive a sufficient condition for the approximate controllability of conformable semilinear systems. Finally, some examples are given to illustrate our theoretical results.