Eigenvalue ratios for the conformable fractional vibrating string equations with single-well densities
Year: 2025
Type: article
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 $ \lambda_n / \lambda_m $, namely$ \frac{\lambda_n}{\lambda_m} \le \left(\frac{n}{m}\right)^2 \quad (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.
Source: AIMS Mathematics
Author: Mengze Gu
Institution: Changsha Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W4416601564