This study develops an efficient numerical method for optimal control problems governed by fractional Volterra integro-differential equations. A new type of polynomials orthogonal with respect to a discrete norm, namely discrete Hahn polynomials, is introduced and its properties investigated. Fractional operational matrices for the orthogonal polynomials are also derived. A direct numerical algorithm supported by the discrete Hahn polynomials and operational matrices is used to approximate solution of optimal control problems governed by fractional Volterra integro-differential equations. Several examples are analyzed and the results compared with those of other methods. The required CPU time assesses the computational cost and complexity of the proposed method.

这项研究为分数沃尔特拉积分微分方程控制的最优控制问题开发了一种有效的数值方法。介绍了一种与离散范数正交的新型多项式，即离散哈恩多项式，并研究了其性质。还导出了用于正交多项式的分数运算矩阵。由离散Hahn多项式和运算矩阵支持的直接数值算法用于近似求解由分数Volterra积分微分方程控制的最优控制问题。分析了几个示例，并将结果与​​其他方法进行了比较。所需的CPU时间评估了所提出方法的计算成本和复杂性。