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A Novel Fractional-Order RothC Model

Author

Listed:
  • Vsevolod Bohaienko

    (Istituto per Applicazioni del Calcolo ‘M.Picone’, National Research Council (CNR), Via Amendola 122/D, 70126 Bari, Italy)

  • Fasma Diele

    (Istituto per Applicazioni del Calcolo ‘M.Picone’, National Research Council (CNR), Via Amendola 122/D, 70126 Bari, Italy)

  • Carmela Marangi

    (Istituto per Applicazioni del Calcolo ‘M.Picone’, National Research Council (CNR), Via Amendola 122/D, 70126 Bari, Italy)

  • Cristiano Tamborrino

    (Istituto di Nanotecnologie ‘NANOTEC’, National Research Council (CNR), Via Monteroni 122/D, 73100 Lecce, Italy)

  • Sebastian Aleksandrowicz

    (Centrum Badan Kosmicznych PAN, Bartycka 18a, 00-716 Warszawa, Poland)

  • Edyta Woźniak

    (Centrum Badan Kosmicznych PAN, Bartycka 18a, 00-716 Warszawa, Poland)

Abstract

A new fractional q -order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h , is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model. Results from real-world experiments show that, by adjusting the fractional order q and the multiplier term ζ ( t , q ) , a better match between simulated and actual data can be achieved compared to the traditional integer-order model.

Suggested Citation

  • Vsevolod Bohaienko & Fasma Diele & Carmela Marangi & Cristiano Tamborrino & Sebastian Aleksandrowicz & Edyta Woźniak, 2023. "A Novel Fractional-Order RothC Model," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1677-:d:1112878
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    References listed on IDEAS

    as
    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    2. Singh, Anup & Das, Subir & Ong, S.H., 2022. "Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 491-500.
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