On Double AL- ughair Transform Partial Technique and Solving Telegraphic Equation

Authors

  • Rakzan Shaker Naji Education for Girls Faculty, Kufa University Najaf, Iraq https://orcid.org/0009-0006-5119-947X
  • Ali Hassan Mohammed Education for Girls Faculty, Kufa University Najaf, Iraq

DOI:

https://doi.org/10.31642/JoKMC/2018/120108

Keywords:

AL-Zughair transform, Double AL-Zughair transform , inverse of double AL-Zughair transform. , partial differential equations (PDEs)

Abstract

In this paper, we developing one of the new transform, namely (AL- ughair transform),was introduced through the study of (Double AL- ughair transform, inverse Double AL- ughair transform), method is introduced used to solve the one dimensional partial differential equations with variable coefficients and then we discussed some examples to illustrate this concept and properties. On the other hand, (Double AL- ughair transform ) was presented for the partial derivatives with two variables  and the transport equation and some other partial equations were solved, which indicates the effectiveness of this transformation in solving them in a quick and simplified manner.

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References

[1] D. G. Duff, Transform Methods for solving Partial Differential Equations, Chapman and Hall/CRC, Boca Raton, F. L. (2004) DOI: https://doi.org/10.1201/9781420035148

[2] A. Estrin & T. J. Higgins, The Solution of Boundary Value Problems by Multiple Laplace Transformation, Journal of the Franklin Institute, 252 (2), 153 – 167, 1951. DOI: https://doi.org/10.1016/0016-0032(51)90950-7

[3] Steven J. Desjardins, R’emi Vaillancourt,” Ordinary Differential Equations Laplace Transforms and Numerical Methods for Engineers”, Spring, Canada, 2011.

[4] Mohammed, A. H., B. A. Sadiq, and AYMAN MOHAMMED HASSAN ALI. “Solving new type of linear equations by using new transformation.” European Academic Research 4.8 (2016): 7035-7048.

[5] Mohammed, Ali Hassan, Baneen Sadeq Mohammed Ali, and Noora Ali Habeeb. “Al-Zughair convolution.” International Journal of Engineering and Information Systems (IJEAIS) 1.8 (2017): 12-21.

[6] H. Eltayeb and A. Kilicman, “On double sumudu transform and double laplace transform,” Malaysian Journal of Mathematical Sciences, vol. 4, no. 1, pp. 17–30, 2010.

[7] A. Kilicman and H. Eltayeb, “A note on integral transforms and partial differential equations,” App. Math. Sc., vol. 4, no. 3, pp. 109–118,2010.

[8] A. Kilicman and H. Eltayeb, “Some remarks on the sumudu and laplace transforms and applications to differential equations,” ISRN Applied Mathematics, doi: 10.5402/2012/591517, 2012. DOI: https://doi.org/10.5402/2012/591517

[9] A. Kilicman and H. E. Gadain, “On the applications of laplace and sumudu transform,” Journal of the Franklin Institute, vol. 347, pp. 848 –862, 2010. DOI: https://doi.org/10.1016/j.jfranklin.2010.03.008

[10] H. Eltayeb and A. Kilicman, “A note on double laplace transform and telegraphic equations,” Abstract and Applied Analysis, vol. 2013. DOI: https://doi.org/10.1155/2013/932578

[11] Y. Singh and H. K. Mandia, “Relationship between double laplace transform and double mellin transform in terms of generalized hypergeometric function with applications,” International Journal of Scientific and Engineering Research, vol. 3, no. 5, 2012.

[12] Emad .A.K. and others” Applying An Extension Al-Zughair Transform on Radioactive Decay Equation” Journal of Mechanics of continua Mathematical sciences ISSN:2454-7190 Vol 14 (2019)pp:528-532. DOI: https://doi.org/10.26782/jmcms.2019.08.00043

[13] Emad .A.K.and others” Applying Al-Zughair Transform on nuclear physics” International Journal of Engineering &Technology9(1)(2020)pp:9-11 DOI: https://doi.org/10.14419/ijet.v9i1.29807

[14] Emad .A.K. and Elaf S.S ” Applying Al-Zughair Transform into some engineering fields ”AIP Conference Proceedings2386,040027(2022). DOI: https://doi.org/10.1063/5.0066911

[15] Gabriel N., "Ordinary Differential Equations" Mathematics Department, Michigan State University, East Lansing, MI, 48824.October.

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Published

2026-01-05

How to Cite

Naji, R. S. ., & Mohammed , A. H. . (2026). On Double AL- ughair Transform Partial Technique and Solving Telegraphic Equation. Journal of Kufa for Mathematics and Computer, 12(1), 56-60. https://doi.org/10.31642/JoKMC/2018/120108

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