This paper investigates the approximate controllability of a semilinear fractional heat equation involving the Caputo derivative of order \(\alpha \in (0,1)\) , incorporating both state and control delays, as well as impulsive effects. The model captures essential memory characteristics and discontinuous external influences, which are common in real-world diffusion phenomena with hereditary and abrupt perturbations. We formulate the system as a mild solution using sectorial operators and the Mittag-Leffler function, and derive sufficient conditions for approximate controllability in the presence of fractional dynamics, time delays, and impulses. The main tools involve semigroup theory, properties of fractional integrals, and fixed point techniques adapted to piecewise continuous functions. This work extends the existing theory by establishing a unified framework that accounts for nonlocality in time, delayed interactions, and discontinuous interventions in fractional partial differential equations. Numerical insights or examples may be presented to illustrate the theoretical findings.