Self-adjoint and non-self-adjoint extensions of symmetric q-Sturm–Liouville operators

A space of boundary values is constructed for minimal symmetric regular and singular q-Sturm– Liouville operators in limit-point and limit-circle cases. A description of all maximal dissipative, maximal accumulative, self-adjoint, and other extensions of such symmetric q-Sturm–Liouville operators is given in terms of boundary conditions

Spectral expansion for impulsive dynamic Sturm–Liouville problems on the whole line

In this paper, an impulsive dynamic Sturm–Liouville problem is studied on the interval (−∞, ∞). A spectral matrix-valued function for this problem is obtained. Parseval equality and an eigenfunction expansion are give

Eigenfunction expansion for impulsive singular Hahn–Dirac system

In this study, a singular impulsive Hahn–Dirac system is studied. A spectral function has been established for this type of system. With the help of this function, the Parseval equation and eigenfunction expansion were obtained

Fractional Dirac system with impulsive conditions

In this article, fractional Dirac systems are considered under impulsive conditions and their basic properties are investigated. In this context, the symmetry, eigenvalues, and eigenfunctions of the system were examined and then the existence and uniqueness of the solutions of the system were proved. Finally, the characteristic function of the system is shown

Impulsive Regular q-Dirac Systems

This article concerns a regular q-Dirac system under impulsive conditions. We study the existence of solutions, symmetry of the corresponding operator, eigenvalues and eigenfunctions of the system. Also we obtain Green’s function and its basic properties

The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators

In this study, the resolvent of the impulsive singular Hahn–Sturm– Liouville operator is considered. An integral representation for the resolvent of this operator is obtained

Impulsive Regular q-Dirac Systems

This article concerns a regular q-Dirac system under impulsive conditions. We study the existence of solutions, symmetry of the corresponding operator, eigenvalues and eigenfunctions of the system. Also we obtain Green’s function and its basic properties

Titchmarsh–Weyl theory for impulsive q -Dirac equation

In this paper, the Titchmarsh–Weyl theory of the impulsive q-Dirac equation is studied

Fractional Dirac system with impulsive conditions

In this article, fractional Dirac systems are considered under impulsive conditions and their basic properties are investigated. In this context, the symmetry, eigenvalues, and eigenfunctions of the system were examined and then the existence and uniqueness of the solutions of the system were proved. Finally, the characteristic function of the system is shown