This paper studies the fractional optimal control problems (FOCPs) with inequality constraints. Using the Caputo definition, an optimization method based on a set of basis functions, namely the fractional-order Bernoulli wavelet functions (F-BWFs), is proposed. The solution is expanded in terms of the F-BWFs with unknown coefficients. In the first step, we convert the inequality conditions to equality conditions. In the second step, we use the operational matrix (OM) of fractional integration and the product OM of F-BWFs, with the help of the Lagrange multipliers technique for converting the FOCPs into an easier one, described by a system of nonlinear algebraic equations. Finally, for illustrating the efficiency and accuracy of the proposed technique, several numerical examples are analysed and the results compared with the analytical or the approximate solutions obtained by other techniques.

中文翻译：

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使用分数阶伯努利小波函数求解具有不等式约束的分数最优控制问题

本文研究了具有不等式约束的分数最优控制问题（FOCPs）。使用 Caputo 定义，提出了一种基于一组基函数的优化方法，即分数阶伯努利小波函数 (F-BWFs)。该解决方案根据系数未知的 F-BWF 进行了扩展。第一步，我们将不等式条件转化为等式条件。在第二步中，我们使用分数积分的运算矩阵 (OM) 和 F-BWF 的乘积 OM，借助拉格朗日乘法器技术将 FOCP 转换为更简单的 FOCP，由非线性代数方程系统描述. 最后，为了说明所提出技术的效率和准确性，