In this article, a new numerical method based on Bernoulli wavelet basis has been applied to give the approximate solution of the fractional optimal control problems. The new operational matrices of multiplication and fractional integration are constructed. The proposed method is applied to reduce the problem to the solution of a system of algebraic equations. The fractional derivative is considered in the Caputo sense. Convergence of the algorithm is proved and some results concerning the error analysis are obtained. Approximate solutions are given and in the cases when we have an exact solution, a comparison with the exact solution is presented to demonstrate the validity and applicability of the proposed method. In addition, we compare the obtained results with the results of other methods. Comparison shows the more accuracy of presented technique in comparison to other published methods.

中文翻译：

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通过新的Bernoulli小波运算矩阵解决分数最优控制问题

在本文中，基于伯努利小波的一种新的数值方法被应用于给出分数最优控制问题的近似解。构造了乘法和分数积分的新运算矩阵。所提出的方法用于将问题减少到代数方程组的解。在Caputo的意义上考虑分数导数。证明了该算法的收敛性，并获得了一些有关误差分析的结果。给出了近似解，并且在我们有一个精确解的情况下，与该精确解进行了比较，以证明该方法的有效性和适用性。另外，我们将获得的结果与其他方法的结果进行比较。