The purpose of this paper is to study the axisymmetric vibrations of circular three-layered sandwich plates with a frequency-dependent fractional viscoelastic core and elastic face sheets. First, the equations of motion and related boundary conditions are derived using the Hamilton's principle for the free vibrations. Then, the governing equations obtained for various boundary conditions are solved and parametric studies are carried out to examine the vibration behavior of circular sandwich plates with a viscoelastic core. The differential transform method (DTM), a well-known semi-analytical-numerical solution technique, is utilized for the eigenvalue analysis. In addition, the finite element (FE) solution obtained with the commercial code ANSYS is added to this comparison. The effect of face and core layer thicknesses and the location of the core layer and core material on the dynamic and damping characteristics of circular sandwich plates with a fractional derivative viscoelastic core is studied in detail.