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The aim of this article is to present a general framework of operational matrix via Shifted Legendre Polynomials (SLOM) for the solution of Fractional Partial Differential Equations (FPDEs) with variable coefficients. A new operational matrix is developed to approximate the solutions of two dimensional FPDEs. By using this operational matrix, a system of algebraic equations is attained. To demonstrate the efficiency and reliability of the proposed method, some numerical examples are conferred and compared with other existing approaches.doi:10.17485/ijst/2017/v10i12/112972 fatcat:e2nyhpfzozgk5d3veyc6v347ae