Spectral expansion for singular conformable fractional Dirac systems

Allahverdiev, Bilender P.; Tuna, Hüseyin

doi:10.1007/s12215-019-00476-3

Cited by 2 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the classical Sturm‐Liouville equation, the integral representation of the resolvent was first proved by H. Weyl in 1910. Similar theorems can be found, eg, in other works . Eckhardt and Teschl gave a comprehensive treatment of Sturm‐Liouville operators whose coefficients are measures, including a full discussion of self‐adjoint extensions and boundary conditions, resolvents, and Weyl‐Titchmarsh‐Kodaira theory.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the resolvent of singular Sturm‐Liouville operators with transmission conditions

Allahverdiev

Tuna

2020

Math Meth Appl Sci

Self Cite

View full text Add to dashboard Cite

In this article, we investigate the resolvent operator of singular Sturm‐Liouville problem with transmission conditions. We obtain integral representations for the resolvent of this operator in terms of the spectral function. Later, we discuss some properties of the resolvent operator, such as Hilbert‐Schmidt kernel property, compactness. Finally, we give a formula in terms of the spectral function for the Weyl‐Titchmarsh function of this problem.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Similar theorems can be found, eg, in other works. [24][25][26][27][28][29][30] Eckhardt and Teschl 31 gave a comprehensive treatment of Sturm-Liouville operators whose coefficients are measures, including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh-Kodaira theory.…”

Section: Introductionmentioning

confidence: 99%

On the resolvent of singular Sturm‐Liouville operators with transmission conditions

Allahverdiev

Tuna

2020

Math Meth Appl Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…The studies on the direct and inverse eigenvalue problems can be viewed from [11,[21][22][23]. Basic spectral features of linear differential operators including conformable derivatives, which inspired our work, were studied by [2,3,5,6,25]. Authors have established an existence and uniqueness theorem for a conformable fractional Dirac system in study [2].…”

Section: Introductionmentioning

confidence: 99%

“…Authors have established an existence and uniqueness theorem for a conformable fractional Dirac system in study [2]. Also they have addresses the existence of a spectral function for a singular conformable Dirac system in [3]. The M-truncated derivative can be employed in studies related to eigenvalue problems and spectral analysis.…”

Section: Introductionmentioning

confidence: 99%

Fractional approach for Dirac operator involving M-truncated derivative

ERCAN

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

View full text Add to dashboard Cite

In this study, we examine the basic spectral information for systems governed by the Dirac equation with distinct boundary conditions, utilizing a modified form of local derivatives known as M-truncated derivative (MTD). The spectral information discussed includes the representation of solutions in the form of integral equations, the asymptotics vector-valued eigenfunctions and eigenvalues, and their normalized forms, all within the context of the MTD method that incorporates truncated Mittag-Leffler functions. This type of MTD provides the features of integer-order operator theory. Also, by virtue of the parameters $\alpha $ and $\gamma$, we analyze and compare the solutions with graphs in terms of different potentials, different eigenvalues and different orders. Thus, the aim of this article is to consider spectral structure of Dirac system in frame of M-truncated derivative by proping with visual analysis.

show abstract

Spectral expansion for singular conformable fractional Dirac systems

Cited by 2 publications

References 29 publications

On the resolvent of singular Sturm‐Liouville operators with transmission conditions

On the resolvent of singular Sturm‐Liouville operators with transmission conditions

Fractional approach for Dirac operator involving M-truncated derivative

Contact Info

Product

Resources

About