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Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials

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  • Meng, Zhijun
  • Yi, Mingxu
  • Huang, Jun
  • Song, Lei

Abstract

In this paper, numerical techniques are presented for solving initial value problems of nonlinear fractional differential equations. The method is implemented by applying alternative Legendre polynomials. The operational matrix of fractional integration and the product for the alternative Legendre polynomials are derived in order to transform the nonlinear equations into a system of algebraic equations. The study of the error analysis of the obtained method is also considered. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

Suggested Citation

  • Meng, Zhijun & Yi, Mingxu & Huang, Jun & Song, Lei, 2018. "Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 454-464.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:454-464
    DOI: 10.1016/j.amc.2018.04.072
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    References listed on IDEAS

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    Cited by:

    1. Wang, Lei & Chen, Yiming & Cheng, Gang & Barrière, Thierry, 2020. "Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Cao, Jiawei & Chen, Yiming & Wang, Yuanhui & Cheng, Gang & Barrière, Thierry, 2020. "Shifted Legendre polynomials algorithm used for the dynamic analysis of PMMA viscoelastic beam with an improved fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Hamid, Muhammad & Usman, Muhammad & Haq, Rizwan Ul & Tian, Zhenfu, 2021. "A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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