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On artificial neural networks approach with new cost functions

Author

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  • Jafarian, Ahmad
  • Measoomy Nia, Safa
  • Khalili Golmankhaneh, Alireza
  • Baleanu, Dumitru

Abstract

In this manuscript, the artificial neural networks approach involving generalized sigmoid function as a cost function, and three-layered feed-forward architecture is considered as an iterative scheme for solving linear fractional order ordinary differential equations. The supervised back-propagation type learning algorithm based on the gradient descent method, is able to approximate this a problem on a given arbitrary interval to any desired degree of accuracy. To be more precise, some test problems are also given with the comparison to the simulation and numerical results given by another usual method.

Suggested Citation

  • Jafarian, Ahmad & Measoomy Nia, Safa & Khalili Golmankhaneh, Alireza & Baleanu, Dumitru, 2018. "On artificial neural networks approach with new cost functions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 546-555.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:546-555
    DOI: 10.1016/j.amc.2018.07.053
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    References listed on IDEAS

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    1. Kostić, Srđan & Stojković, Milan & Prohaska, Stevan, 2016. "Hydrological flow rate estimation using artificial neural networks: Model development and potential applications," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 373-385.
    2. Pakdaman, M. & Ahmadian, A. & Effati, S. & Salahshour, S. & Baleanu, D., 2017. "Solving differential equations of fractional order using an optimization technique based on training artificial neural network," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 81-95.
    3. Zhu, Lei & Xu, Wei-wei, 2016. "The inverse eigenvalue problem of structured matrices from the design of Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1-7.
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    Cited by:

    1. Zafar, Muhammad Hamza & Mansoor, Majad & Abou Houran, Mohamad & Khan, Noman Mujeeb & Khan, Kamran & Raza Moosavi, Syed Kumayl & Sanfilippo, Filippo, 2023. "Hybrid deep learning model for efficient state of charge estimation of Li-ion batteries in electric vehicles," Energy, Elsevier, vol. 282(C).
    2. Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.
    3. Qu, Haidong & She, Zihang & Liu, Xuan, 2021. "Neural network method for solving fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).

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