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Haar wavelet method for approximating the solution of a coupled system of fractional-order integral–differential equations

Author

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  • Xie, Jiaquan
  • Wang, Tao
  • Ren, Zhongkai
  • Zhang, Jun
  • Quan, Long

Abstract

In the current study, a numerical scheme based on the Haar wavelet is proposed to solve a coupled system of fractional-order integral–differential equations. The proposed method is to derive the operational matrix of fractional-order integration, and that is used to transform the main problem to a system of algebraic equations. Additionally, the convergence analysis theorem of this system is rigorously established and the numerical results show that the proposed method is practicable and effective for solving such kinds of problem.

Suggested Citation

  • Xie, Jiaquan & Wang, Tao & Ren, Zhongkai & Zhang, Jun & Quan, Long, 2019. "Haar wavelet method for approximating the solution of a coupled system of fractional-order integral–differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 80-89.
    • Handle: RePEc:eee:matcom:v:163:y:2019:i:c:p:80-89
    DOI: 10.1016/j.matcom.2019.02.010
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    References listed on IDEAS

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    1. Zhao, Fuqiang & Huang, Qingxue & Xie, Jiaquan & Li, Yugui & Ma, Lifeng & Wang, Jianmei, 2017. "Chebyshev polynomials approach for numerically solving system of two-dimensional fractional PDEs and convergence analysis," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 321-330.
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    3. Shokrollahi, Foad & Sottinen, Tommi, 2017. "Hedging in fractional Black–Scholes model with transaction costs," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 85-91.
    4. Pezza, L. & Pitolli, F., 2018. "A multiscale collocation method for fractional differential problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 210-219.
    5. Foad Shokrollahi & Tommi Sottinen, 2017. "Hedging in fractional Black-Scholes model with transaction costs," Papers 1706.01534, arXiv.org, revised Jul 2017.
    6. Saeed, Umer & ur Rehman, Mujeeb, 2015. "Haar wavelet Picard method for fractional nonlinear partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 310-322.
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