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A Numerical Method for Solving Fractional Differential Equations by Using Neural Network

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  • Haidong Qu
  • Xuan Liu

Abstract

We present a new method for solving the fractional differential equations of initial value problems by using neural networks which are constructed from cosine basis functions with adjustable parameters. By training the neural networks repeatedly the numerical solutions for the fractional differential equations were obtained. Moreover, the technique is still applicable for the coupled differential equations of fractional order. The computer graphics and numerical solutions show that the proposed method is very effective.

Suggested Citation

  • Haidong Qu & Xuan Liu, 2015. "A Numerical Method for Solving Fractional Differential Equations by Using Neural Network," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-12, October.
    • Handle: RePEc:hin:jnlamp:439526
    DOI: 10.1155/2015/439526
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    Cited by:

    1. Haddouchi, Faouzi & Samei, Mohammad Esmael, 2024. "Solvability of a generalized ψ-Riemann–Liouville fractional BVP under nonlocal boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 355-377.
    2. Xing Gao & Jinqing Jia & Guoxiong Mei & Xiaohua Bao & Lihua Zhang & Xiaoping Liao, 2022. "A New Prestress Loss Calculation Model of Anchor Cable in Pile–Anchor Structure," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    3. Chi, Xiaoqing & Jiang, Xiaoyun, 2021. "Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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