Baki Keskin

This paper investigates the inverse nodal problem for a Dirac operator with a discontinuity at the midpoint. By means of an asymptotic analysis of the solutions of the associated integral equations, asymptotic formulas for the eigenvalues and nodal points are derived. These results are used to show that the potential functions of the discontinuous Dirac system can be determined from a dense subset of nodal points corresponding to the first component of the eigenfunctions. A constructive reconstruction procedure is then presented to recover the potentials from nodal data. In addition, a numerical approach based on Chebyshev polynomials of the third kind is employed to approximate the potentials. The numerical results indicate that the method yields satisfactory approximations. These results contribute to the study of inverse nodal problems for discontinuous Dirac operators.

This paper deals with an inverse nodal problem for the Dirac differential operator with the discontinuity conditions inside the interval. We obtain a new approach for asymptotic expressions of the solutions and prove that the coefficients of the Dirac system can be determined uniquely by a dense subset of the nodal points (zeros of the first component of the eigenfunction). We also provide an algorithm for constructing the solution of this inverse nodal problem.

This study considers a conformable fractional Dirac-type integral differential system, focusing on its mathematical properties and practical implications. Asymptotic formulas have been derived for the solutions, eigenvalues, and nodes of the problem, providing a deeper understanding of the behavior of the system under varying conditions. These asymptotic results form the basis for analyzing the spectral characteristics and node distribution of the system. In addition, an algorithm is developed that effectively solves the inverse nodal problem and reconstructs the system coefficients from the nodal data.

We consider the integro-differential Dirac operator with parameter-dependent nonlocal integral boundary conditions. We derive the asymptotic expressions for the eigenvalues and the zeros of eigenfunctions (nodal points or nodes) and develop a constructive procedure for solving the inverse nodal problem for this operator.

In this paper we study a partial inverse spectral problem for non-self-adjoint Sturm–Liouville operators with a constant delay and show that subspectra of two boundary value problems with one common boundary condition are sufficient to determine the complex potential. We developed the Horváth’s method in [M. Horváth, On the inverse spectral theory of Schrödinger and Dirac operators, Trans. Amer. Math. Soc. 353 2001, 10, 4155–4171] for the self-adjoint Sturm–Liouville operator without delay into the non-self-adjoint Sturm–Liouville differential operator with a constant delay.

In this article, Dirac-type integro-differential operator with linear functions in the boundary condition is considered. We obtain asymptotic expressions for the solution of the differential system and derive the large eigenvalues and nodal points. We also give a constructive procedure for solving an inverse nodal problem. We prove that a dense subset of the nodes determines the coefficients of the differential part of the operator and gives partial information for the integral part of it.

In this paper, one dimensional conformable fractional Dirac-type integro differential system is considered. The asymptotic formulae for the solutions, eigenvalues and nodal points are obtained. We investigate the inverse nodal problem and give an effective procedure for solving the inverse nodal problem with respect to given a dense subset of nodal points.

In this work, we study the inverse nodal problem for Dirac type integro-differential operator with the boundary conditions dependent spectral parameter polynomially. We prove that dense subset of the nodal points determines the coefficients of differential part of operator and gives partial information for integral part of it.