Electron. J. Differential Equations, Vol. 2021 (2021), No. 62, pp. 1-14.

Smallest eigenvalues for boundary value problems of two term fractional differential operators depending on fractional boundary conditions

Paul W. Eloe, Jeffrey T. Neugebauer

Let n≥2 be an integer, and let n-1<α≤n. We consider eigenvalue problems for two point n-1 ,1 boundary value problems

where 0≤ β ≤n-1 and $D_{0+}^{\alpha}$ and $D_{0+}^{\beta}$ denote standard Riemann-Liouville differential operators. We prove the existence of smallest positive eigenvalues and then obtain comparisons of these smallest eigenvalues as functions of both p and β.

Submitted October 14, 2020. Published July 7, 2021.
Math Subject Classifications: 26A33, 34A08, 34A40, 26D20
Key Words: Riemann-Liouville fractional differential equation; boundary value problem; principal eigenvalue; fractional boundary conditions

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Paul W. Eloe
Department of Mathematics
University of Dayton
Dayton, OH 45469, USA
email: peloe1@udayton.edu
Jeffrey T. Neugebauer
Department of Mathematics and Statistics
Eastern Kentucky University
Richmond, KY 40475, USA
email: Jeffrey.Neugebauer@eku.edu

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