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The issue of fractional derivatives for delaminated and multilayered piezoelectric composite plate supported on a viscoelastic foundation\u2019s 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. 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