The numerical solution of the 2-D time-fractional Sobolev equations is approximated using an efficient local differential quadrature method, in this paper. The time-fractional part of the model equations uses the Liouville-Caputo fractional derivative technique, however, the recommended meshless method is employed for the space derivatives. Test problems are used to undertake numerical experiments. In order to evaluate the effectiveness and accuracy of the suggested meshless method, we compared our outcomes with the exact solution and numerical methods presented in more recent literature. This comparison showed that the proposed method is more efficient computationally and yields excellent performance.