In a variety of applications, such as sensing, vibration control, wind turbine blades, automobile panels, submersible vehicles, and structural health monitoring, smart structures which are made up of laminated composite plates sandwiched between two piezoelectric layers are used. The issue of fractional derivatives for delaminated and multilayered piezoelectric composite plate supported on a viscoelastic foundation's free vibration response has been tackled in this work. A system of differential quadrature and a perturbation method are used to derive and solve the governing equations. Four form functions, the Lagrange interpolation polynomial, the Cardinal Sine function, the Delta Lagrange, and the Regularized Shannon kernel are used in this study to provide new DQM approaches. A numerical system is suggested and tested under a range of support circumstances to determine its accuracy and efficiency, which relies on prior enabling more accurate predictions critical for the design and deployment of intelligent structural systems.