Affiliation:
1. School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 4P4, Canada
Abstract
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.
Reference23 articles.
1. Atkinson, F.V. (1964). Discrete and Continuous Boundary Problems, Academic Press.
2. Fractional Sturm-Liouville eigenvalue problems, I;Dehghan;Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A Mat.,2020
3. Klimek, M., Ciesielski, M., and Blaszczyk, T. (2022). Exact and Numerical Solution of the Fractional Sturm-Liouville Problem with Neumann Boundary Conditions. Entropy, 24.
4. Fractional Sturm Liouville problem;Klimek;Comput. Math. Appl.,2013
5. Variational methods for the fractional Sturm Liouville problem;Klimek;J. Math. Anal. Appl.,2014