This paper presents the extension to viscoelastic cores of a recently proposed variable kinematics (VK) modeling approach, the Sublaminate Generalized Unified Formulation (SGUF). The plate model is defined as a Layer-Wise (LW) assembly of "sublaminates", each composed of an arbitrary number of adjacent plies. An arbitrary approximation across the thickness can be attributed to each displacement component in each sublaminate: ESL or LW descriptions can be used in conjunction with any order of polynomial expansion. This VK approach is particularly effective for sandwich structures, whose strong material mismatch calls for a LW description for the skins and the core, each requiring adequate kinematic assumptions for representing the different mechanical response (e.g., transverse shear in the core, membrane in the skins). Viscoelastic core properties are taken into account through a fractional derivatives (FD) representation of the frequency-dependent material parameters. In order to simulate viscoelastic materials defined within a generalised Maxwell model, the corresponding FD model is first identified by means of a Particle Swarm Optimization process. The in-plane solution for the variable kinematics plate model is defined through a Ritz-based approach. The resulting computational procedure is applied to free-vibration problems of several viscoelastic sandwich panels, and several algorithms for the solution of the non-linear complex eigenvalue problem are devised.