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<p>In this paper, we construct a fractional order aerodynamic model based on the Goman model by introducing the Riemann–Liouville fractional calculus. After approximating the functional derivatives using the backward difference formula, the specific expressions for each parameter in the fractional-order aerodynamic model are derived rigorously. These results provide a theoretical foundation for subsequent numerical approximation and parameter fitting. A fast and highly accurate method for calculating the Riemann–Liouville variable fractional order derivative is proposed for the fractional order aerodynamic model. The proposed model is then validated using several sets of experimental data. The validity of the RL-VFD model proposed in this paper is verified by comparing it with previous FD models through two statistical indicators, root mean square error and coefficient of determination. The simulation results show that the proposed variable fractional derivative aerodynamic model can better express the nonlinear non-stationary aerodynamic characteristics of the airfoil and the aircraft.</p>

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Research on aerodynamic modeling based on Riemann–Liouville fractional calculus

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Jinlei Cui,
  • Lei He,
  • Weiqi Qian,
  • Tun Zhao,
  • Jing Yu,
  • Hai Chen,
  • Jinpei Xiao

摘要

In this paper, we construct a fractional order aerodynamic model based on the Goman model by introducing the Riemann–Liouville fractional calculus. After approximating the functional derivatives using the backward difference formula, the specific expressions for each parameter in the fractional-order aerodynamic model are derived rigorously. These results provide a theoretical foundation for subsequent numerical approximation and parameter fitting. A fast and highly accurate method for calculating the Riemann–Liouville variable fractional order derivative is proposed for the fractional order aerodynamic model. The proposed model is then validated using several sets of experimental data. The validity of the RL-VFD model proposed in this paper is verified by comparing it with previous FD models through two statistical indicators, root mean square error and coefficient of determination. The simulation results show that the proposed variable fractional derivative aerodynamic model can better express the nonlinear non-stationary aerodynamic characteristics of the airfoil and the aircraft.