The Dixmier trace was introduced by Jacques Dixmier in 1966 and its key role in noncommutative geometry was discovered by Connes around 1990 during his development of non-commutative infinitesimal calculus. Remarkably, the Dixmier trace is used to define dimension, integration and has been used along with heat kernel type expansions, to define ‘spectral actions’ for noncommutative quantum field theories. This work concerns a generalization of the Dixmier trace to its fractional counterpart. Some new properties are raised and explored in some details.