Fractional Dirac systems with Mittag-Leffler kernel

Bilender Allahverdiev; Hüseyin Tuna

doi:10.31801/cfsuasmas.1298907

Research Article

Fractional Dirac systems with Mittag-Leffler kernel

Year 2024, Volume: 73 Issue: 1, 1 - 12, 16.03.2024

Bilender Allahverdiev Hüseyin Tuna

https://doi.org/10.31801/cfsuasmas.1298907

Abstract

In this paper, we study some fractional Dirac-type systems with the Mittag–Leffler kernel. We extend the basic spectral properties of the ordinary Dirac system to the Dirac-type systems with the Mittag–Leffler kernel. First, this problem was handled in a continuous form. The self-adjointness of the operator produced by this system, the reality of its eigenvalues, and the orthogonality of the eigenfunctions have been investigated. Later, similar results were obtained by considering the discrete state.

Keywords

Fractional differential equations, Mittag-Leffler kernel, Dirac systems

References

Abdeljawad, T., Baleanu, D., Integration by parts and its applications of a new non-local fractional derivative with Mittag–Leffler nonsingular kernel, J. Nonlinear Sci. Appl., 10(3) (2017), 1098-1107. http://dx.doi.org/10.22436/jnsa.010.03.20
Abdeljawad, T., On Delta and Nabla Caputo fractional differences and dual identities, Discrete Dyn. Nat. Soc., 2013 (2013), Art. ID 406910, 1-12. https://doi.org/10.1155/2013/406910
Abdeljawad, T., Dual identities in fractional difference calculus within Riemann, Adv. Differ. Equ., 2013 (2013), 1-16. https://doi.org/10.1186/1687-1847-2013-36
Atangana, A., Baleanu, D., New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769. https://doi.org/10.2298/TSCI160111018A
Abdeljawad, T., Baleanu, D., Discrete fractional differences with nonsingular discrete Mittag–Leffler kernels, Adv. Differ. Equ., 2016(232) (2016), 1-18. https://doi.org/10.1186/s13662-016-0949-5
Atici, F. M., Eloe, P. W., Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equ., Spec. Ed. I , 2009 (2009), 1-12.
Bas, E., Ozarslan, R., Baleanu, D., Ercan, A., Comparative simulations for solutions of fractional Sturm–Liouville problems with non-singular operators, Adv. Diff. Equ., 2018(350) (2018). https://doi.org/10.1186/s13662-018-1803-8
Ercan, A., On the fractional Dirac systems with non-singular operators, Thermal science, 23(6) 2019, 2159-2168. https://doi.org/10.2298/TSCI190810405E
Erdelyi, A., Book Reviews: Higher Transcendental Functions. Vol. III. Based in Part on Notes Left by Harry Bateman. Science, 122, 290, 1955.
Goodrich, C., Peterson, A. C., Discrete Fractional Calculus, Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-25562-0
Levitan, B. M., Sargsjan, I. S., Sturm–Liouville and Dirac operators. Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1991 (translated from the Russian).
Mert, R., Abdeljawad, T., Peterson, A., A Sturm–Liouville approach for continuous and discrete Mittag–Leffler kernel fractional operators, Discr. Contin. Dynam. System, Series S, 14(7) (2021), 2417-2434. https://doi.org/10.3934/dcdss.2020171
Yalçınkaya, Y., Some fractional Dirac systems, Turkish J. Math., 47 (2023), 110–122. doi:10.55730/1300-0098.3349

Year 2024, Volume: 73 Issue: 1, 1 - 12, 16.03.2024

Bilender Allahverdiev Hüseyin Tuna

https://doi.org/10.31801/cfsuasmas.1298907

Abstract

References

Abdeljawad, T., Baleanu, D., Integration by parts and its applications of a new non-local fractional derivative with Mittag–Leffler nonsingular kernel, J. Nonlinear Sci. Appl., 10(3) (2017), 1098-1107. http://dx.doi.org/10.22436/jnsa.010.03.20
Abdeljawad, T., On Delta and Nabla Caputo fractional differences and dual identities, Discrete Dyn. Nat. Soc., 2013 (2013), Art. ID 406910, 1-12. https://doi.org/10.1155/2013/406910
Abdeljawad, T., Dual identities in fractional difference calculus within Riemann, Adv. Differ. Equ., 2013 (2013), 1-16. https://doi.org/10.1186/1687-1847-2013-36
Atangana, A., Baleanu, D., New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769. https://doi.org/10.2298/TSCI160111018A
Abdeljawad, T., Baleanu, D., Discrete fractional differences with nonsingular discrete Mittag–Leffler kernels, Adv. Differ. Equ., 2016(232) (2016), 1-18. https://doi.org/10.1186/s13662-016-0949-5
Atici, F. M., Eloe, P. W., Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equ., Spec. Ed. I , 2009 (2009), 1-12.
Bas, E., Ozarslan, R., Baleanu, D., Ercan, A., Comparative simulations for solutions of fractional Sturm–Liouville problems with non-singular operators, Adv. Diff. Equ., 2018(350) (2018). https://doi.org/10.1186/s13662-018-1803-8
Ercan, A., On the fractional Dirac systems with non-singular operators, Thermal science, 23(6) 2019, 2159-2168. https://doi.org/10.2298/TSCI190810405E
Erdelyi, A., Book Reviews: Higher Transcendental Functions. Vol. III. Based in Part on Notes Left by Harry Bateman. Science, 122, 290, 1955.
Goodrich, C., Peterson, A. C., Discrete Fractional Calculus, Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-25562-0
Levitan, B. M., Sargsjan, I. S., Sturm–Liouville and Dirac operators. Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1991 (translated from the Russian).
Mert, R., Abdeljawad, T., Peterson, A., A Sturm–Liouville approach for continuous and discrete Mittag–Leffler kernel fractional operators, Discr. Contin. Dynam. System, Series S, 14(7) (2021), 2417-2434. https://doi.org/10.3934/dcdss.2020171
Yalçınkaya, Y., Some fractional Dirac systems, Turkish J. Math., 47 (2023), 110–122. doi:10.55730/1300-0098.3349

There are 13 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Bilender Allahverdiev This is me 0000-0002-9315-4652 Hüseyin Tuna 0000-0001-7240-8687
Publication Date	March 16, 2024
Submission Date	May 18, 2023
Acceptance Date	September 25, 2023
Published in Issue	Year 2024 Volume: 73 Issue: 1

Cite

APA	Allahverdiev, B., & Tuna, H. (2024). Fractional Dirac systems with Mittag-Leffler kernel. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 1-12. https://doi.org/10.31801/cfsuasmas.1298907
AMA	Allahverdiev B, Tuna H. Fractional Dirac systems with Mittag-Leffler kernel. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2024;73(1):1-12. doi:10.31801/cfsuasmas.1298907
Chicago	Allahverdiev, Bilender, and Hüseyin Tuna. “Fractional Dirac Systems With Mittag-Leffler Kernel”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 1 (March 2024): 1-12. https://doi.org/10.31801/cfsuasmas.1298907.
EndNote	Allahverdiev B, Tuna H (March 1, 2024) Fractional Dirac systems with Mittag-Leffler kernel. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 1–12.
IEEE	B. Allahverdiev and H. Tuna, “Fractional Dirac systems with Mittag-Leffler kernel”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 1, pp. 1–12, 2024, doi: 10.31801/cfsuasmas.1298907.
ISNAD	Allahverdiev, Bilender - Tuna, Hüseyin. “Fractional Dirac Systems With Mittag-Leffler Kernel”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (March 2024), 1-12. https://doi.org/10.31801/cfsuasmas.1298907.
JAMA	Allahverdiev B, Tuna H. Fractional Dirac systems with Mittag-Leffler kernel. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:1–12.
MLA	Allahverdiev, Bilender and Hüseyin Tuna. “Fractional Dirac Systems With Mittag-Leffler Kernel”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 1, 2024, pp. 1-12, doi:10.31801/cfsuasmas.1298907.
Vancouver	Allahverdiev B, Tuna H. Fractional Dirac systems with Mittag-Leffler kernel. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):1-12.