Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

Here, we investigate the spectral and oscillation theory for a class of fractional differential equations subject to specific boundary conditions. By transforming the problem into a modified version with a classical structure, we establish the orthogonality properties of eigenfunctions and some majo...

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Bibliographic Details
Published inFractal and fractional Vol. 8; no. 4; p. 238
Main Authors Dehghan, Mohammad, Mingarelli, Angelo B.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2024
Subjects
Analysis
Boundary conditions
Caputo
Derivatives
Differential equations
Eigenvalues
Eigenvectors
Field theory
fractional
Fractional calculus
Integrals
Liouville equations
Orthogonality
Riemann–Liouville
spectral theory
Sturm–Liouville
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Summary:Here, we investigate the spectral and oscillation theory for a class of fractional differential equations subject to specific boundary conditions. By transforming the problem into a modified version with a classical structure, we establish the orthogonality properties of eigenfunctions and some major comparison theorems for solutions. We also derive a new type of integration by using parts of formulas for modified fractional integrals and derivatives. Furthermore, we analyze the variational characterization of the first eigenvalue, revealing its non-zero first eigenfunction within the interior. Our findings demonstrate the potential for novel definitions of fractional derivatives to mirror the classical Sturm–Liouville theory through simple isospectral transformations.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8040238