The purpose of this paper is to suggest a numerical technique to solve fractional variational problems (FVPs). These problems are based on Caputo fractional derivatives. Rayleigh–Ritz method is used in this technique. First we approximate the objective function by the trapezoidal rule. Then, the unknown function is expanded in terms of the Bernstein polynomials. By this method, a system of algebraic equations is driven. We provide examples to show the effectiveness of this technique, which is considered in the current study.

中文翻译：

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求解分数阶变分问题的近似技术

本文的目的是提出一种解决分数变分问题 (FVP) 的数值技术。这些问题基于 Caputo 分数阶导数。在该技术中使用瑞利-里兹方法。首先我们通过梯形规则近似目标函数。然后，根据伯恩斯坦多项式展开未知函数。通过这种方法，可以驱动一个代数方程组。我们提供了一些示例来展示当前研究中考虑的这种技术的有效性。