In this article, Haar wavelet collocation technique is adapted to acquire the approximate solution of fractional Korteweg-de Vries (KdV), Burgers', and KdV–Burgers' equations. The fractional order derivatives involved are described using the Caputo definition. In the proposed technique, the given nonlinear fractional differential equation is discretized with the help of Haar wavelet and reduced to the nonlinear system of equations, which are solved with Newton's or Broyden's method. The proposed method is semi-analytic as it involves exact integration of Caputo derivative. The proposed technique is widely applicable and robust. The technique is tested upon many test problems. The results are computed and presented in the form of maximum absolute errors which show the accuracy, efficiency, and simple applicability of the proposed method.

中文翻译：

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分数阶 Korteweg-de Vries 和 Burgers 方程的 Haar 小波数值解

在本文中，Haar 小波搭配技术适用于获取分数阶 Korteweg-de Vries (KdV)、Burgers 和 KdV–Burgers 方程的近似解。所涉及的分数阶导数使用 Caputo 定义进行描述。在所提出的技术中，给定的非线性分数阶微分方程在 Haar 小波的帮助下被离散化，并简化为非线性方程组，用牛顿或布罗登的方法求解。所提出的方法是半解析的，因为它涉及 Caputo 导数的精确积分。所提出的技术具有广泛的适用性和鲁棒性。该技术在许多测试问题上进行了测试。计算结果并以最大绝对误差的形式呈现，显示精度、效率、