The aeroelastic analysis has become important for aerodynamical model of wind turbine in predicting the wind turbine; such phenomenon is based on aerodynamic performance to have accuracy and feasibility through modeling of fractal and fractional differential techniques. In this context, the mathematical modeling is developed based on fractal and fractional differential techniques for three-dimensional nonautonomous model of a permanent magnet synchronous generator. The fractal and fractional differential techniques so called Caputo, Caputo–Fabrizio and Atangana–Baleanu differential operators have been invoked for the controllability of the stability of system. Numerical schemes for the mathematical model of wind turbine have been established via Adams–Bashforth–Moulton method. The comparative analysis of mathematical model of wind turbine is tackled by means of classical, fractal, fractional and fractal–fractional techniques through chaotic behavior. The role of chaotic oscillations has been depicted on the basis of parametric study of tip speed ratio, pitch angle, drag coefficients, power coefficient, air density and rotor angular speed.

中文翻译：

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分形和分数微分算子对风力机气动模型的数值研究和混沌振荡

气动弹性分析已成为风力机气动模型预测风力机的重要手段；这种现象是基于空气动力学性能，通过分形和分数微分技术的建模具有准确性和可行性。在此背景下，基于分形和分数微分技术开发了永磁同步发电机三维非自主模型的数学建模。分形和分数微分技术被称为 Caputo、Caputo-Fabrizio 和 Atangana-Baleanu 微分算子，用于系统稳定性的可控性。通过 Adams-Bashforth-Moulton 方法建立了风力涡轮机数学模型的数值方案。通过混沌行为，通过经典、分形、分数和分形-分数技术对风力涡轮机的数学模型进行比较分析。在对叶尖速比、桨距角、阻力系数、功率系数、空气密度和转子角速度的参数研究的基础上，已经描述了混沌振荡的作用。