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We study characteristic functions and describe asymptotics of the eigenvalues for the spectral Sturm-Liouville problem on graphs equipped with Robin-Kirhhoff boundary conditions. Also, we show how to recover the coefficients in the Robin…

Spectral Theory · Mathematics 2026-02-17 Yuri Latushkin , Vyacheslav Pivovarchik , Alesia Supranovych

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

Spectral Theory · Mathematics 2021-04-28 Natalia P. Bondarenko

The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using…

General Mathematics · Mathematics 2021-08-12 Shavkat Alimov , Ravshan Ashurov

Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when…

Analysis of PDEs · Mathematics 2020-07-15 Sabrina Roscani , Nahuel Caruso , Domingo Tarzia

In this paper, further to the point interaction method for inverse Sturm-Liouville problems on finite intervals firstly proposed in our previous work, we will continue to generalize this method to the inverse eigenvalue problems for…

Classical Analysis and ODEs · Mathematics 2025-10-13 Min Zhao , Jiangang Qi , Xiao Chen

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

In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential…

Spectral Theory · Mathematics 2016-09-13 Natalia Bondarenko , Chung-Tsun Shieh

In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville…

Mathematical Physics · Physics 2025-08-18 Lung-Hui Chen

We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may…

Classical Analysis and ODEs · Mathematics 2019-12-12 Arran Fernandez , Ceren Ustaoglu

The Telegraph equation $(\partial_{t}^{\rho })^{2}u(x,t)+2\alpha \partial_{t}^{\rho }u(x,t)-u_{xx}(x,t)=f(x,t)$, where $0<t\leq T$ and $0<\rho<1$, with the Riemann-Liouville derivative is considered. Existence and uniqueness theorem for the…

Analysis of PDEs · Mathematics 2023-08-09 Rajapboy Saparbayev

In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…

Classical Analysis and ODEs · Mathematics 2013-04-23 Erdoğan Şen

We consider the Sturm-Liouville operator on the lasso graph with a segment and a loop joined at one point, which has arbitrary length. The Ambarzumyan's theorem for the operator is proved, which says that if the eigenvalues of the operator…

Spectral Theory · Mathematics 2023-06-02 Feng Wang , Chuan-Fu Yang

In this work, we use the \textit{regularized sampling method} to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity…

Numerical Analysis · Mathematics 2020-06-30 Lijing Zhao , Weihua Deng , Jan S Hesthaven

We consider a Sturm-Liouville operator a with integrable potential $q$ on the unit interval $I=[0,1]$. We consider a Schr\"odinger operator with a real compactly supported potential on the half line and on the line, where this potential…

Spectral Theory · Mathematics 2020-01-29 Evgeny Korotyaev

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time…

Spectral Theory · Mathematics 2012-11-14 Jonathan Eckhardt , Gerald Teschl

This paper presents two new classes of M\"untz functions which are called Jacobi-M\"untz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they…

Numerical Analysis · Mathematics 2019-08-02 Hassan Khosravian-Arab , Mohammad Reza Eslahchi

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the…

Numerical Analysis · Mathematics 2009-11-13 Veerle Ledoux , Marnix Van Daele , Guido Vanden Berghe

We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure…

Spectral Theory · Mathematics 2012-11-13 Alexey Fedoseev