The present paper investigates and develops a new technique based on the Chebyshev cardinal functions for solving fractional optimal control problems of a spring-mass-viscodamper system involving the Caputo–Fabrizio fractional operator. Through the way, the new operational matrix of Caputo–Fabrizio fractional operator is achieved for Chebyshev cardinal functions. Moreover, we apply a direct approach for solving the fractional optimal control problem by reducing the original problem to a system of algebraic equations. We also compare this new fractional operator with well known Caputo fractional derivative in the numerical example that shows Caputo–Fabrizio fractional operator may provide better results in terms of settling time of the system.

本文研究和开发了一种基于Chebyshev基数函数的新技术，用于解决涉及Caputo–Fabrizio分数算子的弹簧-质量-粘滞阻尼器系统的分数最优控制问题。通过这种方式，为切比雪夫基数功能实现了Caputo–Fabrizio分数运算符的新运算矩阵。此外，我们通过将原始问题简化为代数方程组，采用直接方法来解决分数最优控制问题。在数值示例中，我们还将该新的分数运算符与众所周知的Caputo分数导数进行了比较，显示出Caputo–Fabrizio分数运算符可能会在系统稳定时间方面提供更好的结果。