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In the present paper, we investigate the fractional analog of the Sturm-Liouville problem on a metric graph using a combination of left Riemann-Liouville and right Caputo fractional derivatives. This combination creates a symmetric and…

Analysis of PDEs · Mathematics 2025-04-29 A. A. Turemuratova , R. Ch. Kulaev , Z. A. Sobirov

In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…

Spectral Theory · Mathematics 2024-11-12 Xiao-Chuan Xu , Yi-Jun Pan

The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the…

Spectral Theory · Mathematics 2017-01-03 Natalia Bondarenko

Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…

Spectral Theory · Mathematics 2016-02-16 Vjacheslav Yurko

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…

Spectral Theory · Mathematics 2020-08-10 Maria Kuznetsova

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…

Spectral Theory · Mathematics 2018-02-08 Natalia Bondarenko , Vjacheslav Yurko

We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl-Titchmarsh theory for these relations.…

Spectral Theory · Mathematics 2012-05-28 Jonathan Eckhardt

The matrix Sturm-Liouville operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm-Liouville operators on geometrical graphs.…

Spectral Theory · Mathematics 2020-07-16 Natalia P. Bondarenko

We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…

Spectral Theory · Mathematics 2020-02-13 Natalia P. Bondarenko

In this article, we first introduce a singular fractional Sturm-Liouville eigen-problems (SFSLP) on unbounded domain. The associated fractional differential operators in these problems are both Weyl and Caputo type . The properties of…

Numerical Analysis · Mathematics 2015-02-20 T. Aboelenen , H. M. El-Hawary

The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…

Numerical Analysis · Mathematics 2016-04-15 Ricardo Almeida , Agnieszka B. Malinowska , M. Luísa Morgado , Tatiana Odzijewicz

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…

Spectral Theory · Mathematics 2021-07-13 S. A. Buterin , M. A. Kuznetsova , V. A. Yurko

We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…

Analysis of PDEs · Mathematics 2026-03-30 Ali Feizmohammadi , Yavar Kian

Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding…

Classical Analysis and ODEs · Mathematics 2014-11-21 Douglas R. Anderson , Richard I. Avery

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

Spectral Theory · Mathematics 2021-07-27 Natalia P. Bondarenko

Very recently, some authors have studied new types of fractional derivatives whose kernels are nonsingular. In this article, we study Sturm-Liouville Equations ($SLEs$) in the frame of fractional operators with Mittag-Leffler kernels. We…

Classical Analysis and ODEs · Mathematics 2018-03-15 Raziye Mert , Thabet Abdeljawad , Allan Peterson

A connection, which shows the dependence of norming constants on boundary conditions, was found using the Gelfand-Levitan method for the solution of inverse Sturm-Liouville problem.

Spectral Theory · Mathematics 2017-05-19 Yuri Ashrafyan , Tigran Harutunyan

The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some…

Spectral Theory · Mathematics 2017-11-16 Chuan-Fu Yang , Natalia P. Bondarenko

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

Analysis of PDEs · Mathematics 2024-10-23 Xiaohua Jing , Zhiyuan Li , Masahiro Yamamoto

The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…

Spectral Theory · Mathematics 2010-10-29 A. M. Savchuk , A. A. Shkalikov