Samira Bonyadi - Mathematics Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
Yaghoub Mahmoudi - Mathematics Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
Mehrdad Lakestani - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Mohammad Jahangiri rad - Mathematics Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

The paper reports a spectral method for generating an approximate solution for the space-time fractional PDEs with variable coefficients based on the spectral shifted Jacobi collocation method in conjunction with the shifted Jacobi operational matrix of fractional derivatives. The spectral collocation method investigates both temporal and spatial discretizations. By applying the shifted Jacobi collocation method, the problem reduces to a system of algebraic equations, which greatly simplifies the problem. Numerical results are given to establish the validity and accuracy of the presented procedure for space-time fractional PDE.

Jacobi polynomials, Operational matrices, space-time PDEs, Collocation method