### A Legendre Computational Matrix Method for Solving High-Order Fractional Differential Equations

#### Abstract

In this paper, a matrix method for the approximate solution of high order fractional differential equations (FDEs) in terms of a truncated Legendre series is presented. The FDEs and its initial or boundary conditions are transformed to matrix equations, which correspond to a system of algebraic equations with unknown Legendre coefficients. The solution of this system yields the Legendre coefficients of the solution formula. Several numerical examples, such as Cauchy and Bagley-Torvik fractional differential equations, are provided to confirm the accuracy and the effectiveness of the proposed method.

doi:10.14456/WJST.2014.45

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