The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a different route, namely, construction of explicit asymptotic approximations for the solutions. As a study case, we consider a problem with left and right Riemann-Liouville derivatives, for which our analysis yields asymptotically sharp estimates for the sequence of eigenvalues and eigenfunctions.

中文翻译：

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分数 Sturm-Liouville 问题中的锐渐近

目前对分数阶 Sturm-Liouville 边值问题的研究主要集中在定性理论和数值方法上，并且最近在这两个方向上都取得了很大进展。本文的目的是探索不同的途径，即为解决方案构建显式渐近近似。作为一个研究案例，我们考虑一个关于左和右黎曼-刘维尔导数的问题，我们的分析产生了对特征值和特征函数序列的渐近尖锐的估计。