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Spectral data of conformable Sturm-Liouville direct problems. (English) Zbl 1461.34050

The paper under review deals with the spectral analysis of conformable Sturm-Liouville problems. For this aim, the authors obtain asymptotic formulas for eigenvalues and normalized eigenfunctions. Also they prove the existence of infinitely many eigenvalues. To illustrate the results, they give an application to the reality of eigenvalues and \(\alpha\)-orthogonality of eigenfunctions for conformable Sturm-Liouville problems.

MSC:

34B24 Sturm-Liouville theory
34B09 Boundary eigenvalue problems for ordinary differential equations
34A08 Fractional ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34L05 General spectral theory of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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