AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM

Mohammad Shahriari; Bahareh Mohammadalipour; Sohrab Bazm; Hanif Mirzaei

AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM

Abstract

In this paper, the fractional Dirac operator with Caputo's fractional derivative is considered. By using Laplace transform, the fractional Dirac operator reduces to an algebraic equation. Then by applying the inverse Laplace transform, we obtain the closed form of the characteristic function according to the two--parameters Mittag--Leffler function. By truncating the series of Mittag-Leffler function, the eigenvalues and the corresponding eigenfunctions are approximated. A convergence analysis for the proposed procedure is given. Finally, the efficiency and simplicity of the method are shown with some examples.

Keywords

Thanks

The authors are thankful to the referees for their valuable comments.

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Mohammad Shahriari ^*
0000-0002-8982-2451
Iran

Bahareh Mohammadalipour This is me
0000-0003-2644-8754
Iran

Sohrab Bazm
0000-0002-1531-6636
Iran

Hanif Mirzaei
0000-0001-8905-9241
Iran

Publication Date

December 6, 2025

Submission Date

December 24, 2024

Acceptance Date

July 7, 2025

Published in Issue

Year 2025 Volume: 15 Number: 12

IZ

https://izlik.org/JA68DH39NF

Cite

RIS / Bibtex

APA

Shahriari, M., Mohammadalipour, B., Bazm, S., & Mirzaei, H. (2025). AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM. TWMS Journal of Applied and Engineering Mathematics, 15(12), 2828-2840. https://izlik.org/JA68DH39NF

AMA

1.Shahriari M, Mohammadalipour B, Bazm S, Mirzaei H. AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM. JAEM. 2025;15(12):2828-2840. https://izlik.org/JA68DH39NF

Chicago

Shahriari, Mohammad, Bahareh Mohammadalipour, Sohrab Bazm, and Hanif Mirzaei. 2025. “AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM”. TWMS Journal of Applied and Engineering Mathematics 15 (12): 2828-40. https://izlik.org/JA68DH39NF.

EndNote

Shahriari M, Mohammadalipour B, Bazm S, Mirzaei H (December 1, 2025) AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM. TWMS Journal of Applied and Engineering Mathematics 15 12 2828–2840.

IEEE

[1]M. Shahriari, B. Mohammadalipour, S. Bazm, and H. Mirzaei, “AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM”, JAEM, vol. 15, no. 12, pp. 2828–2840, Dec. 2025, [Online]. Available: https://izlik.org/JA68DH39NF

ISNAD

Shahriari, Mohammad - Mohammadalipour, Bahareh - Bazm, Sohrab - Mirzaei, Hanif. “AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM”. TWMS Journal of Applied and Engineering Mathematics 15/12 (December 1, 2025): 2828-2840. https://izlik.org/JA68DH39NF.

JAMA

1.Shahriari M, Mohammadalipour B, Bazm S, Mirzaei H. AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM. JAEM. 2025;15:2828–2840.

MLA

Shahriari, Mohammad, et al. “AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 12, Dec. 2025, pp. 2828-40, https://izlik.org/JA68DH39NF.

Vancouver

1.Mohammad Shahriari, Bahareh Mohammadalipour, Sohrab Bazm, Hanif Mirzaei. AN INVESTIGATION OF THE FRACTIONAL DIRAC OPERATOR USING LAPLACE TRANSFORM. JAEM [Internet]. 2025 Dec. 1;15(12):2828-40. Available from: https://izlik.org/JA68DH39NF