In this paper, we construct numerical schemes based on the Lagrange polynomial interpolation to solve Fractional Sturm–Liouville problems (FSLPs) in which the fractional derivatives are considered in the Caputo sense. First, we convert the differential equation with boundary conditions into integral form and discretize the fractional integral to generate a system of algebraic equations in the matrix form. Next, we calculate the set of approximate eigenvalues and corresponding eigenvectors. The eigenfunctions are approximated and some of their properties are investigated. The experimental rate of convergence of numerical calculations for the eigenvalues is reported and the order convergence of the numerical method is obtained. Finally, some examples are presented to illustrate the efficiency and accuracy of the numerical method.

在本文中，我们基于拉格朗日多项式插值构建数值方案，以解决在Caputo意义上考虑分数导数的分数Sturm-Liouville问题（FSLP）。首先，我们将具有边界条件的微分方程转换为积分形式，并将分数积分离散化，以生成矩阵形式的代数方程组。接下来，我们计算一组近似特征值和相应的特征向量。特征函数是近似的，并且研​​究了它们的一些特性。报道了特征值数值计算的实验收敛速度，并获得了数值方法的阶收敛性。最后，通过一些例子说明了数值方法的有效性和准确性。