Homogeneous Robin Boundary Conditions and Discrete Spectrum of Fractional Eigenvalue Problem

6 Pages Posted: 13 Nov 2018

See all articles by Malgorzata Klimek

Malgorzata Klimek

Czestochowa University of Technology

Date Written: July 1, 2018

Abstract

We discuss a fractional eigenvalue problem with the fractional Sturm-Liouville operator mixing the left and right derivatives of order in the range (1/2, 1], subjected to a variant of Robin boundary conditions. The considered differential fractional Sturm-Liouville problem (FSLP) is equivalent to an integral eigenvalue problem on the respective subspace of continuous functions. By applying the properties of the explicitly calculated integral Hilbert-Schmidt operator, we prove the existence of a purely atomic real spectrum for both eigenvalue problems. The orthogonal eigenfunctions’ systems coincide and constitute a basis in the corresponding weighted Hilbert space.

Suggested Citation

Klimek, Malgorzata, Homogeneous Robin Boundary Conditions and Discrete Spectrum of Fractional Eigenvalue Problem (July 1, 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018, Available at SSRN: https://ssrn.com/abstract=3271340 or http://dx.doi.org/10.2139/ssrn.3271340

Malgorzata Klimek (Contact Author)

Czestochowa University of Technology ( email )

ul. Armii Krajowej 19 B
Częstochowa, 42-200
Poland

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