In the present study, the free vibration analysis of piezoelectric composite nanobeams is performed with various boundary conditions. Novel numerical techniques based on quadrature schemes with various test functions are applied with the generalized Caputo kind to solve the boundary value fractional problems. The accuracy and validity of the present analysis are demonstrated by comparing the present results with the previously published ones. Moreover, a parametric analysis is carried out to examine the effect of some material parameters, fractional order derivatives, and geometric dimensions on the vibration attitude of the nanobeam. This parametric study proven the ability of our techniques to provide a solution to most complex fractional differential equations. It is revealed that the fractional differential quadrature methods decrease the time and computational costs.