<p>This paper addresses the existence and uniqueness of mild solutions for a class of non-autonomous semi-linear systems governed by conformable fractional derivatives in Hilbert spaces. By transforming the system into an equivalent integral equation, we apply functional analytic methods, particularly fixed-point techniques, to establish well-posedness. The study further develops evolution operators adapted to the conformable framework, which play a central role in characterizing the system’s dynamics. Additionally, sufficient conditions for exact null controllability are derived by leveraging suitable estimates and control function construction. A detailed numerical example is included to demonstrate the applicability of the theoretical findings.</p>