A new fractional-order Dickson functions are introduced for solving numerically fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel. The type of fractional derivative in the proposed problems is the Atangana–Baleanu–Caputo fractional derivative. In the process of the method, we use fractional-order Dickson functions and their properties to provide an accurate computational technique for calculating operational matrices, at first. Then, with the help of operational matrices and the Lagrange multiplier method, these problems are reduced to a system of algebraic equations. At last, to demonstrate the effectiveness of the new method, we enforce the proposed algorithm for several examples.

引入了新的分数阶Dickson函数，以解决涉及Mittag-Leffler非奇异核的数值分数最优控制和变分问题。在所提出的问题中，分数导数的类型是Atangana–Baleanu–Caputo分数导数。在该方法的过程中，首先，我们使用分数阶Dickson函数及其性质来提供一种精确的计算技术来计算运算矩阵。然后，借助运算矩阵和拉格朗日乘数法，将这些问题简化为代数方程组。最后，为了证明新方法的有效性，我们将提出的算法用于几个示例。