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Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm

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  • Bohaienko, Vsevolod
  • Gladky, Anatolij
  • Romashchenko, Mykhailo
  • Matiash, Tetiana

Abstract

The paper studies a ψ-Caputo space-time-fractional moisture transport model stated in terms of water head. We consider a functional parameter of ψ-Caputo derivatives in power and sigmoid forms and use particle swarm optimization algorithm to identify model’s parameters. Input data for the identification were acquired on the irrigated field in the South of Ukraine within one irrigation cycle. Direct problems were solved using a finite-difference scheme. In these conditions, application of a fractional model with the classic Caputo derivative allowed more than ~ 2-times lowering of average absolute error compared to the integer-order model. The usage of functional parameter in power form allowed up to 19% accuracy enhancement compared to the classic Caputo derivative while the usage of sigmoid function up to 2.6-times lowers the error. Such behaviour remains when predicting soil moisture dynamics within the following irrigation cycles.

Suggested Citation

  • Bohaienko, Vsevolod & Gladky, Anatolij & Romashchenko, Mykhailo & Matiash, Tetiana, 2021. "Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320306184
    DOI: 10.1016/j.amc.2020.125665
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    References listed on IDEAS

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    1. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
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    Cited by:

    1. Zhang, Tao & Lu, Zhong-rong & Liu, Ji-ke & Chen, Yan-mao & Liu, Guang, 2023. "Parameter estimation of linear fractional-order system from laplace domain data," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Bohaienko, V.O., 2021. "Accuracy and speed of splitting methods for three-dimensional space–time fractional diffusion equation with ψ-Caputo derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 226-240.
    3. Xing, Liwen & Zhao, Lu & Cui, Ningbo & Liu, Chunwei & Guo, Li & Du, Taisheng & Wu, Zongjun & Gong, Daozhi & Jiang, Shouzheng, 2023. "Apple tree transpiration estimated using the Penman-Monteith model integrated with optimized jarvis model," Agricultural Water Management, Elsevier, vol. 276(C).

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