In this study, the spectral analysis of conformable Sturm–Liouville problems (CSLPs) are investigated in detail and to that end, the spectral analysis of classical Sturm–Liouville (SL) differential problems move to conformable analysis obtaining the representation of solutions and from this point of view asymptotic forms of spectral data, such as eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Moreover, we compare the solutions by means of illustrations with different arbitrary orders, different potential functions, different eigenvalues and so, we evaluate the behaviors of eigenfunctions. We give an important application to the reality of eigenvalues and \(\alpha \)-orthogonality of eigenfunctions for CSLPs defined by Abdeljawad and Al-Refai (Complexity vol 2017, Article ID 3720471, 2017) in the last section.

在本研究中，详细研究了相容Sturm-Liouville问题（CSLP）的频谱分析，为此，经典Sturm-Liouville（SL）微分问题的频谱分析转向了相容分析，从而获得了解决方案的表示形式，并由此光谱数据的观点渐近形式，例如特征函数，特征值，规范常数和归一化特征函数。因此，我们证明了无限多个特征值的存在。此外，我们通过具有不同任意阶数，不同势函数，不同特征值的插图来比较解，因此，我们评估了特征函数的行为。我们对特征值和\（\ alpha \）的现实给出了重要的应用上一节中由Abdeljawad和Al-Refai定义的CSLP的本征函数的正交性（复杂性2017年，文章ID 3720471,2017年）。