The aim of this article is to investigate an efficient computational method for solving distributed‐order fractional optimal control problems. In the proposed method, a new Riemann‐Liouville fractional integral operator for the Bernstein wavelet is given. This approach is based on a combination of the Bernstein wavelets basis, fractional integral operator, Gauss‐Legendre numerical integration, and Newton's method for solving obtained system. Easy implementation, simple operations, and accurate solutions are the essential features of the proposed method. The error analysis of the proposed method is carried out. Examples reveal the applicability of the proposed technique.

中文翻译：

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伯恩斯坦小波的分布阶分数最优控制问题的数值研究

本文的目的是研究解决分配阶分数最优控制问题的有效计算方法。在提出的方法中，给出了伯恩斯坦小波的新的黎曼-利维尔分数积分算子。该方法基于伯恩斯坦小波基，分数积分算子，高斯莱格朗德数值积分和牛顿法求解获得的系统的组合。易于实施，简单操作和准确的解决方案是该方法的基本特征。对提出的方法进行了误差分析。实例揭示了所提出技术的适用性。