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Year 2023, Volume: 11 Issue: 1, 61 - 69, 30.04.2023

Abstract

References

  • [1] Allahverdiev B. P. and Tuna H., One-dimensional q-Dirac equation, Math. Meth. Appl. Sci.; 402017:7287ñ7306.
  • [2] Annaby M. H. and Mansour Z. S., q-Fractional Calculus and Equations, Lecture Notes in Mathematics 2056, Springer, Berlin, 2012.
  • [3] Bairamov E., and Solmaz ¸S., Scattering theory of Dirac operator with the impulsive condition on whole axis, Math. Meth. Appl. Sci. 44 (9) (2021), 7732-7746.
  • [4] Bashirov A. E., Kurpinar E. M. and Ozyapici A., Multiplicative calculus and its applications, J. Math. Anal.. Appl. 337 (1) (2008),
  • [5] Ernst T., The History of q-Calculus and a New Method, U. U. D. M. Report (2000):16, ISSN1101-3591, Department of Mathematics, Uppsala University, 2000.
  • [6] Goktas S., Kemaloglu H. and Yilmaz E., Multiplicative conformable fractional Dirac system, Turkish J. Math. 46 (2022), 973-990.
  • [7] Goktas S., A new type of SturmñLiouville equation in the nonNewtonian calculus, J. Funct. Spaces 5203939 (2021), 1-8.
  • [8] Grossman M., An introduction to Non-Newtonian calculus, Intern. J. Math. Edu. Sci. Techn. 10 (4) (1979), 525-528.
  • [9] Grossman M. and Katz R., Non-Newtonian calculus, Pigeon Cove, MA: Lee Press, 1972.
  • [10] Gulsen T., Yilmaz E. and Goktas S., Multiplicative Dirac system, Kuwait J. Sci. 2022. doi:10.48129/kjs.13411.
  • [11] Kac V. and Cheung P., Quantum Calculus, Springer, 2002.
  • [12] Levitan B. M. and Sargsjan I.S., SturmñLiouville and Dirac operators, Math. Appl. (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991.
  • [13] Mamedov, K. R. and Akcay, O., Inverse problem for a class of Dirac operators by the Weyl function, Dyn. Syst. Appl. 26 (1) (2017), 183- 196.
  • [14] Mukhtarov O. Sh., Olgar H. and Aydemir K., Resolvent operator and º spectrum of new type boundary value problems, Filomat 29 (7) (2015), 1671-1680.
  • [15] Thaller B., The Dirac Equation. Springer-Verlag, Berlin Heidelberg, 1992.
  • [16] Weidmann J., Spectral Theory of Ordinary Di§erential Operators, Lecture Notes in Mathematics 1258. Springer: Berlin, 1987.
  • [17] Yalcin N. and Celik E., Solution of multiplicative homogeneous linear di§erential equations with constant exponentials, New Trends Math. Sci. 6 (2) (2018), 58-67. 15
  • [18] Yener G. and Emiroglu I., A q-analogue of the multiplicative calculus: qmultiplicative calculus, Discr. Contin. Dynam. Syst.-Ser. S 8 (6) (2015), 1435-1450.
  • [19] Zettl A., SturmñLiouville Theory, Mathematical Surveys and Monographs, 121. American Mathematical Society: Providence, RI, 2005.

$q$-Multiplicative Dirac System

Year 2023, Volume: 11 Issue: 1, 61 - 69, 30.04.2023

Abstract

In this study, the classical Dirac equation was investigated on the basis of $q$-multiplicative calculus. We discuss some spectral properties of the $q$-multiplicative Dirac system, such as formally self-adjointness, and orthogonality of eigenfunctions. Finally, Green's function for this system has been reconstructed.

References

  • [1] Allahverdiev B. P. and Tuna H., One-dimensional q-Dirac equation, Math. Meth. Appl. Sci.; 402017:7287ñ7306.
  • [2] Annaby M. H. and Mansour Z. S., q-Fractional Calculus and Equations, Lecture Notes in Mathematics 2056, Springer, Berlin, 2012.
  • [3] Bairamov E., and Solmaz ¸S., Scattering theory of Dirac operator with the impulsive condition on whole axis, Math. Meth. Appl. Sci. 44 (9) (2021), 7732-7746.
  • [4] Bashirov A. E., Kurpinar E. M. and Ozyapici A., Multiplicative calculus and its applications, J. Math. Anal.. Appl. 337 (1) (2008),
  • [5] Ernst T., The History of q-Calculus and a New Method, U. U. D. M. Report (2000):16, ISSN1101-3591, Department of Mathematics, Uppsala University, 2000.
  • [6] Goktas S., Kemaloglu H. and Yilmaz E., Multiplicative conformable fractional Dirac system, Turkish J. Math. 46 (2022), 973-990.
  • [7] Goktas S., A new type of SturmñLiouville equation in the nonNewtonian calculus, J. Funct. Spaces 5203939 (2021), 1-8.
  • [8] Grossman M., An introduction to Non-Newtonian calculus, Intern. J. Math. Edu. Sci. Techn. 10 (4) (1979), 525-528.
  • [9] Grossman M. and Katz R., Non-Newtonian calculus, Pigeon Cove, MA: Lee Press, 1972.
  • [10] Gulsen T., Yilmaz E. and Goktas S., Multiplicative Dirac system, Kuwait J. Sci. 2022. doi:10.48129/kjs.13411.
  • [11] Kac V. and Cheung P., Quantum Calculus, Springer, 2002.
  • [12] Levitan B. M. and Sargsjan I.S., SturmñLiouville and Dirac operators, Math. Appl. (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991.
  • [13] Mamedov, K. R. and Akcay, O., Inverse problem for a class of Dirac operators by the Weyl function, Dyn. Syst. Appl. 26 (1) (2017), 183- 196.
  • [14] Mukhtarov O. Sh., Olgar H. and Aydemir K., Resolvent operator and º spectrum of new type boundary value problems, Filomat 29 (7) (2015), 1671-1680.
  • [15] Thaller B., The Dirac Equation. Springer-Verlag, Berlin Heidelberg, 1992.
  • [16] Weidmann J., Spectral Theory of Ordinary Di§erential Operators, Lecture Notes in Mathematics 1258. Springer: Berlin, 1987.
  • [17] Yalcin N. and Celik E., Solution of multiplicative homogeneous linear di§erential equations with constant exponentials, New Trends Math. Sci. 6 (2) (2018), 58-67. 15
  • [18] Yener G. and Emiroglu I., A q-analogue of the multiplicative calculus: qmultiplicative calculus, Discr. Contin. Dynam. Syst.-Ser. S 8 (6) (2015), 1435-1450.
  • [19] Zettl A., SturmñLiouville Theory, Mathematical Surveys and Monographs, 121. American Mathematical Society: Providence, RI, 2005.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bilender Paşaoğlu 0000-0002-9315-4652

Hüseyin Tuna 0000-0001-7240-8687

Publication Date April 30, 2023
Submission Date July 19, 2022
Acceptance Date September 6, 2022
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Paşaoğlu, B., & Tuna, H. (2023). $q$-Multiplicative Dirac System. Konuralp Journal of Mathematics, 11(1), 61-69.
AMA Paşaoğlu B, Tuna H. $q$-Multiplicative Dirac System. Konuralp J. Math. April 2023;11(1):61-69.
Chicago Paşaoğlu, Bilender, and Hüseyin Tuna. “$q$-Multiplicative Dirac System”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 61-69.
EndNote Paşaoğlu B, Tuna H (April 1, 2023) $q$-Multiplicative Dirac System. Konuralp Journal of Mathematics 11 1 61–69.
IEEE B. Paşaoğlu and H. Tuna, “$q$-Multiplicative Dirac System”, Konuralp J. Math., vol. 11, no. 1, pp. 61–69, 2023.
ISNAD Paşaoğlu, Bilender - Tuna, Hüseyin. “$q$-Multiplicative Dirac System”. Konuralp Journal of Mathematics 11/1 (April 2023), 61-69.
JAMA Paşaoğlu B, Tuna H. $q$-Multiplicative Dirac System. Konuralp J. Math. 2023;11:61–69.
MLA Paşaoğlu, Bilender and Hüseyin Tuna. “$q$-Multiplicative Dirac System”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 61-69.
Vancouver Paşaoğlu B, Tuna H. $q$-Multiplicative Dirac System. Konuralp J. Math. 2023;11(1):61-9.
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