An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives was obtained in Yang and Srivastava (Commun Nonlinear Sci Numer Simul 29(1–3):499–504, 2015). In this paper, we obtain the numerical solution of damped forced oscillator problems by employing the operational matrix of integration of Bernoulli orthonormal polynomials. The operational matrix of integration is determined with the help of the integral operator on Bernoulli orthonormal polynomials. Numerical examples of two different problems of spring are given to delineate the performance and perfection of this approach and compared the results with the exact solution.

中文翻译：

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一种利用伯努利积分积分矩阵解决阻尼强迫振荡器问题的有效算法

在Yang和Srivastava中获得了由局部分数导数描述的分形介质中的自由阻尼振动的线性振荡器的渐近摄动解（Commun Nonlinear Sci Numer Simul 29（1-3）：499-504，2015）。在本文中，我们通过使用伯努利正交多项式积分的运算矩阵来获得阻尼强迫振荡器问题的数值解。积分的操作矩阵是借助Bernoulli正交多项式上的积分算子确定的。给出了两个不同弹簧问题的数值示例，以描述该方法的性能和完善性，并将结果与​​精确解进行比较。