An estimation for the unknown source term in the time-fractional diffusion equation from measurement data by the alternating direction method of multipliers (ADMM) is considered. The considered model involves a Caputo fractional derivative of order
. The inverse source problem is transformed into an optimal control formulation with two distinct cost functions, namely least squares fitting and the -norm. For its resolution, we use the method for all kinds of cost functions. Finally, the efficiency and accuracy of the present method are illustrated by some numerical examples.