New analytical results for Laguerre polynomials based on the Emad–Sara transform

Mahdi, Ahlam Abdulkareem; Flayyih, Rusul Ahmed; Malik, Nada Hadi; Kuffi, Emad Abbas

doi:10.47974/JIM-2554

Open Access Research Article

New analytical results for Laguerre polynomials based on the Emad–Sara transform

^*Ahlam Abdulkareem MahdiCorresponding authorahlamalfaisaly@gmail.comGeneral Directorate of Education Najaf, Ministry of EducationNajaf, IraqView full profile → , Rusul Ahmed Flayyihmskmrtdy588@gmail.comGeneral Directorate of Education Thi-Qar, Ministry of EducationThi-Qar, IraqView full profile → , Nada Hadi Maliknadah.alardhi@student.uokufa.edu.iqGeneral Directorate of Education Najaf, Ministry of EducationNajaf, IraqView full profile → , Emad Abbas Kuffiemad.Kuffi@uomustansisiyah.edu.iqDepartment of MathematicsCollege of Basic EducationMustansiriyah UniversityBaghdad, IraqView full profile →

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pp. 1617–1623Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2554XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2554
Pages:: 1617–1623

Abstract

An Emad–Sara transform be an effective mathematical technique for simplifying and solving differential equations arising in applied mathematics and engineering sciences. By converting differential operators into algebraic forms, this transform facilitates the analytical treatment of complex problems and improves solution efficiency. In this paper, the Emad–Sara transform is employed to analyze Laguerre polynomials of arbitrary order, and several of their transform properties are derived. Furthermore, the proposed approach is apply to solutions for ordinary differential equation involving Laguerre polynomials, demonstrating the practical utility of the transform in handling polynomial-based differential models. The obtained results confirm that the Emad–Sara transform provides a systematic and reliable framework for simplifying the solution process while preserving analytical accuracy. This study highlights the potential of the Emad–Sara transform as a valuable tool for solving polynomial-based differential equations and supports its applicability in mathematical and engineering applications.

Keywords

ES-integral transform Inverse estransform Cryptography Cryptosystem Encryption Decryption

Subject Classifications

33C4544A10

References

[1] S. F. Maktoof, E. Kuffi, and E. S. Abbas, “Emad-Sara transform: A new integral transform,” Journal of Interdisciplinary Mathematics, vol. 24, no. 7, pp. 1985–1994 (2021).‏
[2] E. A. Kuffi, E. S. Abbas, and S. F. Maktoof, “Solving the beam deflection problem using Al-Tememe transforms,” J. Mech. Continua Math. Sci., vol. 14, no. 4, pp. 519–527 (2019), doi: 10.26782/jmcms.2019.08.00042.
[3] E. A. Kuffi, A. H. Mohammed, A. Q. Majde, and E. S. Abbas, “Applying al-Zughair transform on nuclear physics,” International Journal of Engineering & Technology, vol. 9, no. 1, pp. 9–11 (2020).‏
[4] E. Kuffi, E. Sabah Abbas, and S. Obeid Mebayet, “Al-Tememe transform in solving developed missile automatic control problem,” International Journal of Engineering and Technology, vol. 7, no. 4, pp. 6565–6567 (2019), doi: 10.14419/ijet.v7i4.28919.
[5] H. K. Dass, R. Verma, and R. Verma, Introduction to Engineering Mathematics, 13th ed. New Delhi, India: S. Chand & Company Ltd., p. 680 (2025).
[6] D. Verma, “Analyzing Laguerre polynomial by Aboodh transform,” ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), vol. 4, pp. 14–16 (2020).
[7] D. Verma, “Elzaki transform approach to differential equations with Leguerre polynomial,” International Research Journal of Modernization in Engineering Technology and Science (IRJMETS), vol. 2, pp. 244–248 (2020).‏
[8] D. Verma and A. P. Singh, “Solving differential equations including Leguerre polynomial via Laplace transform,” International Journal of Trend in Scientific Research and Development (IJTSRD), vol. 4, pp. 1016–1019 (2020).‏

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