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A two-dimensional Chebyshev wavelets approach for solving the Fokker-Planck equations of time and space fractional derivatives type with variable coefficients

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  • Xie, Jiaquan
  • Yao, Zhibin
  • Gui, Hailian
  • Zhao, Fuqiang
  • Li, Dongyang

Abstract

In the current study, we consider the numerical solutions of the Fokker-Planck equations of time and space fractional derivative type with variable coefficients. The proposed method is based on the two-dimensional Chebyshev wavelet basis together with their corresponding operational matrices of fractional-order integration. The convergence analysis of the proposed method is rigorously established. Numerical tests are carried out to confirm the effectiveness and feasibility of the proposed scheme.

Suggested Citation

  • Xie, Jiaquan & Yao, Zhibin & Gui, Hailian & Zhao, Fuqiang & Li, Dongyang, 2018. "A two-dimensional Chebyshev wavelets approach for solving the Fokker-Planck equations of time and space fractional derivatives type with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 197-208.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:197-208
    DOI: 10.1016/j.amc.2018.03.040
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    References listed on IDEAS

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    1. Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
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    Cited by:

    1. Wang, Jiao & Xu, Tian-Zhou & Wang, Gang-Wei, 2018. "Numerical algorithm for time-fractional Sawada-Kotera equation and Ito equation with Bernstein polynomials," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 1-11.
    2. 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).
    3. 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).
    4. 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).
    5. Jiaquan Xie & Yongjiang Zheng & Zhongkai Ren & Tao Wang & Guangxian Shen, 2019. "Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions," Complexity, Hindawi, vol. 2019, pages 1-10, December.
    6. Zheng, Wei & Zhang, Zhiming & Sun, Fuchun & Lam, Hak Keung & Wen, Shuhuan, 2022. "Stability analysis and robust controller design for systems with mixed time-delays and stochastic nonlinearity via cone complementarity linearization," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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