A New Algorithm based on Shifted Legendre Polynomials for Fractional Partial Differential Equations

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.