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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations

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  • Qingxue Huang
  • Fuqiang Zhao
  • Jiaquan Xie
  • Lifeng Ma
  • Jianmei Wang
  • Yugui Li

Abstract

In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.

Suggested Citation

  • Qingxue Huang & Fuqiang Zhao & Jiaquan Xie & Lifeng Ma & Jianmei Wang & Yugui Li, 2017. "Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-12, January.
    • Handle: RePEc:hin:jnddns:8630895
    DOI: 10.1155/2017/8630895
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