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Quasilinearized Semi-Orthogonal B-Spline Wavelet Method for Solving Multi-Term Non-Linear Fractional Order Equations

Author

Listed:
  • Can Liu

    (School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China)

  • Xinming Zhang

    (School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China)

  • Boying Wu

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China)

Abstract

In the present article, we implement a new numerical scheme, the quasilinearized semi-orthogonal B-spline wavelet method, combining the semi-orthogonal B-spline wavelet collocation method with the quasilinearization method, for a class of multi-term non-linear fractional order equations that contain both the Riemann–Liouville fractional integral operator and the Caputo fractional differential operator. The quasilinearization method is utilized to convert the multi-term non-linear fractional order equation into a multi-term linear fractional order equation which, subsequently, is solved by means of semi-orthogonal B-spline wavelets. Herein, we investigate the operational matrix and the convergence of the proposed scheme. Several numerical results are delivered to confirm the accuracy and efficiency of our scheme.

Suggested Citation

  • Can Liu & Xinming Zhang & Boying Wu, 2020. "Quasilinearized Semi-Orthogonal B-Spline Wavelet Method for Solving Multi-Term Non-Linear Fractional Order Equations," Mathematics, MDPI, vol. 8(9), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1549-:d:411379
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    References listed on IDEAS

    as
    1. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    2. Zheng, Yunying & Zhao, Zhengang & Cui, Yanfen, 2019. "The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 257-269.
    3. Lai, Qinghua & Diao, Zhijun & Kong, Lingli & Adidharma, Hertanto & Fan, Maohong, 2018. "Amine-impregnated silicic acid composite as an efficient adsorbent for CO2 capture," Applied Energy, Elsevier, vol. 223(C), pages 293-301.
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