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

Authors

  • Mohamed Meabed KHADER Department of Mathematics, Faculty of Science, Benha University, Benha
  • Ahmed Saied HENDY Department of Mathematics, Faculty of Science, Benha University, Benha

Keywords:

Ordinary fractional differential equations, shifted Legendre polynomials, Caputo derivatives, computational matrix method, cauchy equations, Bagley-Torvik 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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Author Biographies

Mohamed Meabed KHADER, Department of Mathematics, Faculty of Science, Benha University, Benha

Department of Mathematics

Ahmed Saied HENDY, Department of Mathematics, Faculty of Science, Benha University, Benha

Department of Mathematics

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Published

2013-10-31

How to Cite

KHADER, M. M., & HENDY, A. S. (2013). A Legendre Computational Matrix Method for Solving High-Order Fractional Differential Equations. Walailak Journal of Science and Technology (WJST), 11(4), 289–305. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/389