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Prediction of high‑speed debris motion in the framework of time‑fractional model: theory and validation


[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ 2 ] Instytut Budownictwa, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.7] Civil engineering, geodesy and transport

Year of publication


Published in

Archives of Civil and Mechanical Engineering

Journal year: 2023 | Journal volume: vol. 23 | Journal number: iss. 1

Article type

scientific article

Publication language


  • High-speed debris motion
  • Fractional derivatives
  • Equation of motion

EN In this work, a newly proposed fractional derivative framework is used for the prediction of high-speed debris motion. The paper focuses on the mathematical formulation of the equation of motion, in which the damping term is generalised using the fractional derivative. The capacity of the proposed approach to predict the motion of debris is justified by the experimental results. Furthermore, the mathematical formulation has been verified by extensive parametric studies on spherical projectiles. The general conclusion is that the elaborated formulation is more reliable compared to the classical approach or, in other words, the fractional viscous damping term (proportional to the fractional velocity of debris) provides a better description of the complexity of the real drag force.

Date of online publication


Pages (from - to)

46-1 - 46-21





Article Number: 46

License type

CC BY (attribution alone)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Ministry points / journal


Impact Factor

4,4 [List 2022]

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