Controllability of Differential Systems with the General Conformable Derivative

In this paper, the controllability of differential systems with the general conformable derivative is studied. By elaborating the rank criterion and the conformable Gram criterion, sufficient and necessary conditions to investigate that a linear general conformable system is null completely controllable are given. We obtain a full generalization to the general conformable fractional-order system case. In addition, Krasnoselskii’s fixed point theorem to obtain a complete controllability result for a semilinear general conformable system is applied.