This work aims to study the vibration analysis of nonlocal plates utilizing space-fractional mechanics. Riesz? Caputo fractional derivative is used to define nonlocality and the frequency spectrum and mode shapes of the plate with one clamped edge and three free edges (CFFF) are carried out for different values of the fractional continua order (a) and the length scale parameter (1). The 3-D vibration analysis is obtained by well-known Ritz energy method. The frequencies are obtained for different values of fractional material properties (a and 1). Moreover, the modes shapes and absolute differences between classical and fractional eigenvectors for the first nine frequencies are presented by using contour plots. The main contribution of the paper is that the nonlocal approach utilizing the fractional calculus gives better results compared to the experimental outcomes than the classical local theory. The overall conclusion is that fractional mechanics establishes a new model for nonlocal vibration analysis.