In this article, the fractal‐fractional (FF) version of the fifth‐order KdV equation is introduced. The shifted Vieta‐Fibonacci (VF) polynomials are generated and adopted to establish a simple and accurate numerical method for solving this equation. To this end, the operational matrices of ordinary and FF derivatives of these polynomials are obtained in explicit forms. These matrices together with the series expansion of the shifted VF polynomials are mutually utilized to convert the original equation into a system of algebraic equations which is much easier. Some numerical examples are examined to show the power and accuracy of the method.

中文翻译：

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分形-分数阶五阶KdV方程的移位Vieta-Fibonacci多项式

本文介绍了五阶KdV方程的分形（FF）版本。生成移位的Vieta-Fibonacci（VF）多项式，并将其用于建立简单而准确的数值方法来求解该方程。为此，以显式形式获得这些多项式的普通和FF导数的运算矩阵。这些矩阵与移位的VF多项式的级数展开共同用于将原始方程式转换为代数方程式系统，这非常容易。检查了一些数值示例，以显示该方法的功效和准确性。