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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 2

Some properties of the Jost solutions and scattering function of a multiplicative Dirac system

Güler Başak Öznur(GAZI UNIVERSITY)0000-0003-4130-5348
Güher Gülçehre Özbey(MIDDLE EAST TECHNICAL UNIVERSITY)0000-0002-1326-4545
Yelda Aygarküçükevcilioğlu(ANKARA UNIVERSITY)0000-0002-5550-3073
Rabia Aktaş Karaman(ANKARA UNIVERSITY)0000-0002-7811-8610
Sayfa
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Yayın Tarihi
2025-12-30
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Moreover, we define the scattering function of the system.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we deal with a multiplicative Dirac system by giving Jost solutions, Jost functions and multiplicative integral representations of the solutions of this system.
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Temel Bulgular & Veri:We also present asymptotic representations for Jost solutions and Jost functions.
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Sonuç & Katkı:Moreover, we define the scattering function of the system.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:multiplicative calculus · scattering function · Jost solution

Abstract

In this study, we deal with a multiplicative Dirac system by giving Jost solutions, Jost functions and multiplicative integral representations of the solutions of this system. We also present asymptotic representations for Jost solutions and Jost functions. Moreover, we define the scattering function of the system.

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Bu Makaleye Atıf Yap

Öznur, G. B., Özbey, G. G., Aygarküçükevcilioğlu, Y., Karaman, R. A. (2025). Some properties of the Jost solutions and scattering function of a multiplicative Dirac system. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1716685

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Kaynakça (29)

  1. E. Bairamov, Y. Aygar and M. Olgun, Jost solution and the spectrum of the discrete Dirac systems, Bound. Value Probl. 306571, 2010.
  2. E. Bairamov and A.O. Çelebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Q. J. Math. 50, 371-384, 1999.
  3. E. Bairamov and T. Köprübaşı, Eigenparameter dependent discrete Dirac equations with spectral singularities, Appl. Math. Comput. 215 (12), 4216-4220, 2010.
  4. E. Bairamov and S. Solmaz, Spectrum and scattering function of the impulsive discrete Dirac systems, Turkish J. Math. 42 (6), 3182-3194, 2018.
  5. A.E. Bashirov, E. M. Kurpınar and A. Özyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (1), 36-48, 2008.
  6. A. Bashirov, E. Mısırlı and Y. Tandogdu, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. 26, 425-438, 2011.
  7. A. Bashirov and M. Rıza, Complex multiplicative calculus, arXiv preprint arXiv:1103.1462, 2011.
  8. F. Benford, The law of anomalous numbers, Proc. Amer. Philos. Soc. 551-572, 1938.
  9. K. Boruah, and B. Hazarika, G-calculus, TWMS J. Appl. Eng. Math. 8 (1), 94-105, 2018.
  10. A.F. Çakmak and F. Başar, Some new results on sequence spaces with respect to non-Newtonian calculus, J. Inequal. Appl. 1-17, 2012.
  11. M. Cheng and Z. Jiang, A new class of production function model and its application, J. Syst. Sci. Inf. 4 (2), 177-185, 2016.
  12. D. Filip and C. Piatecki, A non-Newtonian examination of the theory of exogenous economic growth, Math. Aterna 4 (2), 101-117, 2014.
  13. L. Florack and H. Van Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging Vision 42, 64-75, 2012.
  14. M.G. Gasymov, and B.M. Levitan, The inverse problem for the Dirac system, Doklady Akademii Nauk 167 (5), 967-970, 1966.
  15. S. Göktaş, A New Type of Sturm-Liouville equation in the non-Newtonian calculus, J. Funct. Spaces 1, 5203939, 2021.
  16. S. Göktaş, H. Kemaloglu and E. Yılmaz, Multiplicative conformable fractional Dirac system, Turkish J. Math. 46 (3), 973-990, 2022.
  17. S. Göktaş, E. Yılmaz and A.C. Yar, Multiplicative derivative and its basic properties on time scales, Math. Methods Appl. Sci. 45 (4), 2097-2109, 2022.
  18. M. Grossman, An introduction to non-Newtonian calculus, Internat. J. Math. Ed. Sci. Tech. 10 (4), 525-528, 1979.
  19. M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pgeon Cove, 1979.
  20. T. Gülşen, E. Yılmaz and S. Göktaş, Multiplicative Dirac system, Kuwait J. Sci. 49 (3), 1-11, 2022.
  21. B.M. Levitan and I.S. Sargsjan, Sturm-Liouville and Dirac Operators, Kluwer Academic Publishers Group, Dordrecht, 1991.
  22. S. Özcan, Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex functions, AIMS Mathematics 5 (2), 1505-1518, 2020.
  23. A. Slavik, Product Integration, Its History and Applications, Matfyzpress, Prague, 2007.
  24. D. Stanley, A multiplicative calculus, Primus 4, 310-326, 1999.
  25. V. Volterra and B. Hostinsky, Operations Infinitesimales Linears, Gauthier-Villars, Paris, 1938.
  26. N. Yalçın, The solutions of multiplicative Hermite differential equation and multiplicative Hermite polynomials, Rend. Circ. Mat. Palermo (2) 70, 9-21, 2021.
  27. N. Yalçın, E. Çelik and A. Gökdogan, Multiplicative Laplace transform and its applications, Optik 127 (20), 9984-9995, 2016.
  28. N. Yalçın and M. Dedetürk, Solutions of multiplicative ordinary differential equations via the multiplicative differential transform method, AIMS Mathematics 6 (4), 3393- 3409, 2021.
  29. E. Yılmaz, Multiplicative Bessel equation and its spectral properties, Ric. Mat. 13 (3), 1289-1305, 2024.