In this work, the exponential stability of the nonlocal fractional heat equation is studied. The fractional Laplacian is defined via a singular integral. Using the spectral properties of the fractional Laplacian and a state-decomposition. The feedback control is build taking account the first N modes and an observer defined via a bounded operator. Different kind of configurations are studied to mention, interior controller and interior observation, interior controller and exterior observation. Using the recent result about simplicity of the eigenvalues \cite{fall2023generic}, some of our stabilization results are valid for s ∈ (0, 1), in particular for s ∈ (0, 1/2) in which case the fractional heat equation is not null controllable.