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Neural Network Method for Solving Time-Fractional Telegraph Equation

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  • Wubshet Ibrahim
  • Lelisa Kebena Bijiga

Abstract

Recently, the development of neural network method for solving differential equations has made a remarkable progress for solving fractional differential equations. In this paper, a neural network method is employed to solve time-fractional telegraph equation. The loss function containing initial/boundary conditions with adjustable parameters (weights and biases) is constructed. Also, in this paper, a time-fractional telegraph equation was formulated as an optimization problem. Numerical examples with known analytic solutions including numerical results, their graphs, weights, and biases were also discussed to confirm the accuracy of the method used. Also, the graphical and tabular results were analyzed thoroughly. The mean square errors for different choices of neurons and epochs have been presented in tables along with graphical presentations.

Suggested Citation

  • Wubshet Ibrahim & Lelisa Kebena Bijiga, 2021. "Neural Network Method for Solving Time-Fractional Telegraph Equation," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, May.
    • Handle: RePEc:hin:jnlmpe:7167801
    DOI: 10.1155/2021/7167801
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    Cited by:

    1. Li, Jin & Su, Xiaoning & Zhao, Kaiyan, 2023. "Barycentric interpolation collocation algorithm to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 340-367.
    2. Hajimohammadi, Zeinab & Baharifard, Fatemeh & Ghodsi, Ali & Parand, Kourosh, 2021. "Fractional Chebyshev deep neural network (FCDNN) for solving differential models," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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