@article{Gu2025, 
author = {Mengze Gu},
title = {Eigenvalue ratios for the conformable fractional vibrating string equations with single-well densities},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27235-27246},
keywords = {eigenvalue ratio, conformable fractional, Sturm-Liouville, Prüfer transformation, single-well},
url = {https://www.sciopen.com/article/10.3934/math.20251197},
doi = {10.3934/math.20251197},
abstract = {In this paper, we investigated in a class of Sturm-Liouville vibrating string problems involving conformable fractional derivatives and studied the behavior of their eigenvalue ratios. Under the assumptions that the potential function is of single-barrier type or the density function is of single-well type, we rigorously established the optimal upper bound for the eigenvalue ratios        λ    n        /        λ    m  , namely               λ      n              λ      m        ≤            (              n        m            )        2      (  n  >  m  )  .Moreover, we showed that equality holds if and only if the density or the potential is constant. Our novelty was in extending the classical Sturm–Liouville eigenvalue inequalities to the conformable fractional setting.}
}