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Galoitica: Journal of Mathematical Structures and Applications

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Online: 2834-5568
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Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 11Issue 1PP: 12-24 • 2024

On Some Results about Complex Order Bessel's Equation

Arwa Hajjari 1*
1Cairo University, Department of Mathematics, Cairo, Egypt
* Corresponding Author.
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Open Access & Copyright

© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: October 22, 2023 Revised: February 27, 2024 Accepted: June 24, 2024

Abstract

In this paper, we derive the Bessel's equation of complex order (n + i) from the classical well-known Bessel's equation. In addition, we generalize that recurrence relation from Bessel's equation of order (n) to Bessel equation of complex order (n + i). On the other hand, we present an algorithm to solve the novel complex order equation with many illustrated examples that explain the validity of our approach.

Keywords

Bessel's equation complex order differential equation partial derivation

References

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[6]       Kreyszig E. "Advanced Engineering Mathematics", Wiley, Springer,
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[7]       Luke, Y. L. Integrals of Bessel functions. Courier Corporation, (2014)

[8]       Markel E. G., "Bessel Functions and Equations of Mathematical Physics", Supervisor, Judith Rivas Ulloa, Leioa, 25 June (2015)

[9]       Mclachlan N. W. "Bessel Functions for Engineers", 2nd Edition, Oxford University, Press, London, (1955).

[10]    Okrasinski W., L. Płociniczak, "A Note on Fractional Bessel Equation and Its Asymptotics", Fract. Calc. Appl. Anal., 16 (2013).

[11]    Robin W., "Ladder-operator Factorization and the Bessel Differential Equations", Math. Forum, 9 (2014).

[12]    Thukral A. K. "Factorials of Real Negative and Imaginary Numbers-A new Perspetive", Published (2014).

[13]    Khosravian-Arab, H., Dehghan, M., and Eslahchi, M.R., Generalized Bessel’s functions: Theory and thier applications. Math Meth Appl. Sci., 1–22, 2017.

Cite This Article

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Hajjari, Arwa. "On Some Results about Complex Order Bessel's Equation." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 1, 2024, pp. 12-24. DOI: https://doi.org/10.54216/GJMSA.0110102
Hajjari, A. (2024). On Some Results about Complex Order Bessel's Equation. Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 1), 12-24. DOI: https://doi.org/10.54216/GJMSA.0110102
Hajjari, Arwa. "On Some Results about Complex Order Bessel's Equation." Galoitica: Journal of Mathematical Structures and Applications Volume 11, no. Issue 1 (2024): 12-24. DOI: https://doi.org/10.54216/GJMSA.0110102
Hajjari, A. (2024) 'On Some Results about Complex Order Bessel's Equation', Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 1), pp. 12-24. DOI: https://doi.org/10.54216/GJMSA.0110102
Hajjari A. On Some Results about Complex Order Bessel's Equation. Galoitica: Journal of Mathematical Structures and Applications. 2024;Volume 11(Issue 1):12-24. DOI: https://doi.org/10.54216/GJMSA.0110102
A. Hajjari, "On Some Results about Complex Order Bessel's Equation," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 1, pp. 12-24, 2024. DOI: https://doi.org/10.54216/GJMSA.0110102
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