The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions to this problem is of great importance. Here, we describe how the fractional Sturm-Liouville eigenvalue problem can be formulated as a constrained fractional variational principle and show how such formulation can be used in order to approximate the solutions. Numerical examples are given, to illustrate the method.

中文翻译：

---

求解分数阶离散/连续 Sturm-Liouville 问题的变分方法

分数 Sturm-Liouville 特征值问题出现在许多情况下，例如，在求解来自物理和工程应用的异常扩散方程时。因此，获得该问题的解或解的近似值是非常重要的。在这里，我们描述了分数 Sturm-Liouville 特征值问题如何表述为约束分数变分原理，并展示如何使用这种公式来逼近解。给出了数值例子来说明该方法。