In this paper, a weighted meshless spectral radial point interpolation method (MSRPIM) is implemented for the numerical solutions of a class of multi-term time fractional advection-diffusion problems with spatial and temporal dispersion. In the proposed methodology, meshless shape functions are used for discretization in space. These functions are generated via radial basis functions (RBFs) and point interpolation method. Weighted theta-scheme and first order finite differences together with a simple quadrature rule are employed for the discretization of time fractional derivatives. Efficiency and accuracy of the formulated method is validated in terms of number of nodal points N, time-step size tau and weight parameter theta is an element of [0,1]. Quality of the computed solutions are checked using E-infinity, E-2 and E-rms error norms. Stability of the proposed method is analyzed theocratically and validated computationally, which is an important task of the current paper. Simulations reveal very good accuracy for both 1D and 2D test problems having constants and variable coefficients. (C) 2018 Elsevier Ltd. All rights reserved.