In this paper, we consider a class of fractional Sturm-Liouville problems, in which the second order derivative is replaced by the Caputo fractional derivative. The Laplace transform method is applied to obtain algebraic equations. Then, the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems are obtained numerically. We provide a convergence analysis for given method. Finally, the simplicity and efficiency of the numerical method is shown by some examples.

中文翻译：

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拉普拉斯变换的分数阶Sturm-Liouville问题特征值和特征函数的数值研究

在本文中，我们考虑了一类分数阶Sturm-Liouville问题，其中二阶导数被Caputo分数阶导数代替。应用拉普拉斯变换方法获得代数方程。然后，数值获得分数Sturm-Liouville问题的特征值和特征函数。我们提供给定方法的收敛性分析。最后，通过一些例子说明了数值方法的简单性和有效性。