In this paper, an attractive reliable analytical technique is implemented for constructing numerical solutions for the fractional Lienard’s model enclosed with suitable nonhomogeneous initial conditions, which are often designed to demonstrate the behavior of weakly nonlinear waves arising in the oscillating circuits. The fractional derivative is considered in the Atangana–Baleanu–Caputo sense. The proposed technique, namely, reproducing kernel Hilbert space method, optimizes numerical solutions bending on the Fourier approximation theorem to generate a required fractional solution with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some applications. The acquired results are numerically compared with the exact solutions in the case of nonfractional derivative, which show the superiority, compatibility, and applicability of the presented method to solve a wide range of nonlinear fractional models.

中文翻译：

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LIENARD方程ATANGANA-BALEANU-CAPUTO模型的分段最优分数再生核解及收敛性分析

在本文中，实施了一种有吸引力的可靠分析技术，用于构建包含适当非齐次初始条件的分数 Lienard 模型的数值解，这些初始条件通常用于演示振荡电路中产生的弱非线性波的行为。在 Atangana-Baleanu-Caputo 意义上考虑分数导数。所提出的技术，即再现核希尔伯特空间方法，优化了在傅里叶逼近定理上弯曲的数值解，以生成具有快速收敛形式的所需分数解。通过测试一些应用程序验证了所提出方法的影响、容量和可行性。在非分数导数的情况下，将获得的结果与精确解进行数值比较，