Abstract:This paper studies the Noether symmetry and corresponding conserved quantity for fractional Birkhoffian systems in terms of Caputo fractional derivatives. Firstly, the fractional Pfaff action is defined within Caputo fractional derivatives. The fractional Birkhoff’s equations and corresponding transversality conditions are also established. Secondly, based on the invariance of the Pfaff action under the infinitesimal transformations, the conditions of invariance are given under a special oneparameter group of infinitesimal transformations without transforming the time as well as a general oneparameter group with transforming the time, respectively. Finally, according to the notion of fractional conserved quantity presented by Frederico and Torres, the Noether theorem for the fractional Birkhoffian systems is constructed, which states the relationship between a fractional Noether symmetry and a fractional conserved quantity.